Apple and IBM today announced a broad partnership to help companies deploy wireless devices and business-specific applications to run on them.

The combination brings together two historical competitors — who decades ago struggled to dominate the nascent market for personal computers — on the next wave of computing in business: Mobile devices with access to complex data running in the cloud.

In an interview with Re/code at Apple’s headquarters in Cupertino, Calif., Apple CEO Tim Cook and IBM CEO Ginni Rometty described the tie-up as one that only the two companies could deliver.

“If you were building a puzzle, they would fit nicely together with no overlap,” Cook said of the relationship. “We do not compete on anything. And when you do that you end up with something better than either of you could produce yourself.”

Calling Apple the “gold standard for consumers,” Rometty said the team-up will allow the two giants to address significant opportunities facing large businesses. “We will get to remake professions and unlock value that companies don’t yet have,” she said. “We’re addressing serious issues that before this had been inhibiting deployment of wireless in the enterprise.”

The move will also allow IBM to bring to bear its investments in big data and analytics plus cloud computing services and mobility. Last year it made a significant bet around developing mobile software for the enterprise with an initiative it called MobileFirst. In working with Apple, it has created an extension, dubbed MobileFirst, for iOS.

The partnership got favorable initial reviews from investors in after-hours trading, with IBM up almost two percent and Apple up about 1.50 percent.

The deal calls for IBM and Apple to develop more than 100 industry-specific applications that will run on the iPhone and iPad, including applications for security, analyzing corporate data and managing the devices themselves. Apple will add a new class of service to its AppleCare program and support aimed at enterprise customers. IBM will continue to support other wireless operating systems including Google’s Android.

IBM will also begin to sell iPhones and iPads to its corporate customers and will devote more than 100,000 people, including consultants and software developers, to the effort. Enterprise applications will in many cases run on IBM’s cloud infrastructure or on private clouds that it has built for its customers. Data for those applications will co-exist with personal data like photos and personal email that will run on Apple’s iCloud and other cloud services.

Apple has never made much noise about its enterprise sales and has famously shied away from having a dedicated enterprise sales force. In teaming up with IBM, Cook said, Apple is getting the best of both worlds. Were Apple to fully embrace its potential opportunity in the enterprise it might have to build a new division to the company. In teaming up with IBM it won’t have to go that far.

“We’re good at building a simple experience and in building devices,” Cook said. “The kind of deep industry expertise you would need to really transform the enterprise isn’t in our DNA. But it is in IBM’s.”

Still, since the launch of the iPhone in 2007 and of the iPad in 2010, the company has quietly emerged as a powerhouse supplier of wireless devices to the world’s largest companies. Cook frequently cites the statistic that 98 percent of the Fortune 500 are either testing or actively deploying iOS devices for use by their employees.

And its list of corporate customers is long, including Nestle, FedEx, Deutsche Bank, Johnson Controls, Luxottica, American Airlines, Barclay’s, Cisco Systems, GE and NASA, each of which has deployed tens of thousands of iPhones and iPads among their employees and executives.

The workplace trend known as “bring your own device,” or BYOD, has been especially kind to Apple. Companies have increasingly allowed employees to use their personal devices for work email and to access other data. According to the research firm IDC, iPhones accounted for 82 percent of smartphones in use at U.S. corporations and 36 percent globally; iPads accounted for 73 percent of tablets in use at U.S. corporations and 39 percent around the world.

Another important indicator of the heft of Apple’s presence in the enterprise market is the number of software vendors that have embraced it, which is practically all of them. SAP, Oracle, Netsuite and Salesforce.com were all quick to adapt their business applications to the iPhone and iPad. And practically every enterprise-focused startup — Tidemark, New Relic, Box and others — have been iPhone- and iPad-ready practically from day one.

Apple and IBM will collaborate on building a new class of applications specifically tailored for certain industries, including retail, health care, banking, travel and transportation. The first of those applications will be available in the fall and will be released into next year.

Here are Rometty and Cook talking about the initiative with CNBC’s Josh Lipton: