* New Finnish firm and Foxconn to make Nokia-branded phones

* Nokia, focused on network equipment, to get royalties

* Microsoft sells entry-level phone business to HMD/Foxconn (Adds Breakingviews link, updates Nokia share price)

By Jussi Rosendahl

HELSINKI, May 18 (Reuters) - The Nokia name will return to the mobile phone market after a company backed by one of its former executives teamed up with manufacturer Foxconn to buy the rights to the brand for mobile devices.

Nokia, once the world's biggest maker of mobile phones, was wrongfooted by the rise of smartphones and eclipsed by Apple and Samsung. It sold its entire handset business to Microsoft Corp in 2014 and now focuses on telecoms network equipment.

But it held on to its phone patents with a view to eventually striking a licensing deal, though it had to wait due to a non-compete deal with Microsoft.

Nokia said on Wednesday it had signed an exclusive 10-year licensing agreement for newly formed Finnish company HMD global Oy to create Nokia-branded smartphones and tablets. HMD is owned by Smart Connect LP, a private equity fund run by former Nokia executive Jean-Francois Baril, and its management.

The products will be made by Taiwan's Foxconn and Nokia will receive an undisclosed royalty on sales, covering both brand and intellectual property rights.

Microsoft announced simultaneously it would sell its entry-level phones business to HMD and Foxconn subsidiary FIH Mobile for $350 million.

Nokia, whose global market share in handsets peaked at around 40 percent in 2008, said its brand remained widely recognised, especially in developing markets.

"The areas where we believe the brand is strongest are Asia, South America and parts of Europe. Clearly China will be one of the target markets," Ramzi Haidamus, chief executive of the Nokia Technologies unit, told Reuters.

Nokia stock rose 2.9 percent to 4.67 euros.

"Nokia seems to have put together a very elegant deal in order to maximize the potential to drive some revenue from the handset business, with no risk in terms of hardware," said Ben Wood, an analyst at research firm CCS Insight.

"The brand is strong in the feature phone space, but does it stand for a cutting-edge future proof smartphone? That's unclear. ... It's a brand that has lost its lustre," he added.

HMD, which will focus on branding and design in the partnership with Foxconn, said it would put 500 million euros ($564 million) into marketing over the next three years.

Nokia declined to provide revenue targets related to the licensing deal, nor a timetable for new devices, which will use Google's Android platform. The deal between Microsoft, Foxconn and HMD is expected to close in the second half of 2016.

Jukka Oksaharju, a strategist at brokerage Nordnet, said annual licensing revenues for Nokia would likely be in the tens of millions.

Microsoft has struggled with phones after the 2014 deal with Nokia, and last year it wrote off $7.5 billion from the business. Microsoft said on Wednesday it would continue to develop its Lumia smartphones.

($1 = 0.8868 euros)

(Additional reporting by Tuomas Forsell; Editing by Jason Neely and Mark Potter)