As Chief Executive Tim Cook shifts executive responsibilities around at Apple Inc., AAPL 1.85% Eddy Cue is emerging as one of the biggest beneficiaries.

A member of Apple's old guard, the 23-year company veteran rose through the ranks as co-founder Steve Jobs's right-hand man for new areas like e-commerce and media. But at a company dominated by hardware and operating systems, Mr. Cue was on the periphery and known largely for cajoling media companies to sign on to Apple's iTunes service.

Now the affable executive, a 48-year-old Miami native of Cuban descent, has become a prime architect of Apple's software strategy and one of the most important product voices at a company where no clear chief product visionary has emerged since Mr. Jobs's death last year.

Apple's Eddy Cue pictured in February 2011. REUTERS

The Expansion of Cue's Empire January 2001: Launched iTunes

July 2008: Launched App Store

April 2010: Launched iBooks

October 2011: Launched iCloud

August 2011: Took over iAd

October 2012: Took over Maps and Siri

As senior vice president of Internet Software and Services, Mr. Cue has lately managed crises related to Apple's mobile maps and iCloud and iMessage outages. He has taken on iBooks and the iAd advertising service and oversees Apple's App Store, which has more than 700,000 apps. He urged Mr. Cook and others that Apple should develop a smaller iPad based on his own usage of a seven-inch tablet, which Mr. Jobs previously denounced.

When iPhone software chief Scott Forstall was ousted last month, Mr. Cue inherited two of Apple's newest Internet services: Maps and the voice-activated assistant Siri.

Apple's Inner Circle The Apple Evolution From the Apple II to the iPad Mini More photos and interactive graphics

The ascent solidifies Mr. Cue's role as one of the chief deputies to Mr. Cook, who has surrounded himself with several close advisers without elevating one to a clear number two. Mr. Cue has the loyalty and admiration of many longtime employees, who respect that he was with Apple during the dark days before Mr. Jobs began his turnaround of the company in the late 1990s.

Mr. Cue is also a champion of the Apple way: Entering new areas patiently and slowly and preaching the need to put the customer first. To negotiating partners, he epitomizes the company's penchant for secrecy with a poker face that media companies scramble to decipher.

That patient approach faces new pressure. Apple's dominance in smartphones and tablets is under threat as competitors quickly catch up.

Investors are questioning how much longer Apple can maintain its growth and its unrivaled status as a technology trendsetter.

Amid the shift, Mr. Cue's online businesses have become more strategic as consumers select devices based more on what they can do. ITunes, the largest business Mr. Cue oversees, brought in $2.1 billion in Apple's most recent quarter, or 5.8% of overall revenue.

Mr. Cue "is in charge of all the most important services if Apple wants to grow," said Anthony Soohoo, a former CBS Corp. media executive who negotiated with Mr. Cue and now runs a San Francisco-based media-app company, Rumpus Inc.

Mr. Cue couldn't be reached for comment and Apple didn't make him available for an interview.

Mr. Cue, who lives in Los Altos, Calif., with his wife, cuts a low profile and avoids the Silicon Valley social scene. He isn't the showman Mr. Jobs was or that marketing chief Phil Schiller has become; indeed, despite coaching, Mr. Cue has often confided to colleagues that he's uncomfortable on stage. And he sometimes looks it, glancing down at prompters and pausing more than other slick Apple presenters.

Like Mr. Jobs, he is more a strategist and tactician than manager, say people who have worked closely with him, staying focused on a few top priorities and clearing the next product launch.

After giving employees lots of leeway, Mr. Cue will often swoop in to get things done himself, they say, paying little attention to smaller projects or personnel matters.

This week, Mr. Cue faces a test of how well Apple can keep up in online services with the launch of a new desktop version of iTunes, which is expected as soon as Thursday.

The new iTunes has been delayed a month by engineering issues that required parts to be rebuilt, according to people who have seen it.

The delay comes at a challenging time for Apple. ITunes was a pioneer in digital media, and its share of the paid music download business stood at 64% in the second quarter.

But it now faces competition from rivals like Pandora Media Inc. and Spotify Ltd., which enable users to subscribe to their services and stream music without downloading it. In contrast, iTunes requires people to download media files, although it streams video content to Apple TV.

Mr. Cue is still proceeding cautiously with streaming, preaching his trademark patient approach. The new version of iTunes, dubbed iTunes 11, is more closely integrated with iCloud and resembles the mobile version.

It will allow people to stream music, movies and TV shows they have purchased from Apple from one Apple device to another via the iCloud syncing service without downloading them again. Apple has only offered the function for music in the past through iTunes Match. But computer, tablet and phone users will still have to download the file initially and pay a la carte.

Russ Crupnick, senior vice president of industry analysis for NPD, said the competition isn't hurting Apple yet because the iTunes user base is so big. But "streaming starts to pose a greater risk to iTunes" over time, as it becomes more ubiquitous and convenient in places like cars, he said.

Mr. Cue doesn't seem fazed by the challenges ahead and has seemed upbeat about the future, said people who have spoken to him recently.

Employees single him out as the rare senior Apple manager who likes to make small talk and discuss sports. (Mr. Cue is a Duke University basketball fanatic, and his office is full of photos of the team.)

Employees appreciate that he doesn't shy from acknowledging mistakes head-on by saying things like "We really f—ed up," said people who know him.

Mr. Cue gained credibility at Apple by fixing some of the company's flops, including the MobileMe data syncing service. He re-launched the failed service as iCloud in 2011.

The iCloud launch required major investment in data center technologies outside Apple's expertise, and former employees recall development was rocky.

But Mr. Cue stayed calm and told employees he had confidence in them, one of those people said. Apple said iCloud now has more than 200 million users, roughly half the size of iTunes.

Mr. Cue has also shown a willingness to break from Apple's habit of building everything itself, with some positive results.

In 1999, he helped convince Apple to work with Akamai Technologies Inc. on new streaming functions for its QuickTime video software, recalls Paul Sagan, CEO of Akamai and a longtime Apple partner. (Apple later invested in Akamai, which delivers Internet content.)

Since then, Mr. Cue has displayed an instinct for doing what the customer wants, not what's technically possible. "He would say: No one would want to do that," Mr. Sagan said. "He takes a really direct approach."

Like other Apple senior executives, Mr. Cue has stepped into the limelight more since the death of Mr. Jobs. The two were close and Mr. Jobs trusted Mr. Cue to negotiate partnerships, placing a phone call to a media chief only when it was required to seal the deal.

Mr. Cue is an avid music listener like Mr. Jobs and likes artists including Bruce Springsteen.

One media executive recently remarked that when asking Mr. Cue for promotion in the App Store as part of a broader deal, he would often say: "I have to check with Steve." Now, he just decides himself.

Media remains a tricky area for Mr. Cue. While the company has made progress expanding iTunes, Apple's attempt to break into the living room, which Mr. Cue is overseeing, has stalled, according to people familiar with the matter.

Apple has been in talks with cable companies about a set-top box for watching television for years, only making some progress recently. And some iTunes initiatives, like a Ping social networking service, flopped.

Mr. Cue has been reorganizing his team. He was involved in pushing out the executive who oversaw Apple's new mapping service, Richard Williamson, about two weeks ago, according to people briefed on that matter.

He also recently tried to recruit help for his expanded portfolio, including from outside the company, said people close to his group.

In recent weeks, Mr. Cue also promoted longtime iTunes business executive Robert Kondrk to vice president, other people close to the division said.

Write to Jessica E. Lessin at jessica.lessin@wsj.com