CEO Satya Nadella, said the final price Microsoft is paying may be "slightly higher" than the US$7.5 billion announced in September.
About 30,000 employees will transfer to Microsoft in Redmond, Washington state, as part of the deal.
Microsoft, the world's largest software maker, is gaining a device business on which it hopes to build and begin to catch up with Apple and Google in the tablet and mobile phone markets.
But Nokia is left seeking a turnaround for its network-equipment business and is said to be considering the division's head, Rajeev Suri, as chief executive officer.
Purchase of the unprofitable mobile division makes Microsoft the world's second-largest maker of mobile phones with about 14 percent of the market, according to researcher IDC. Samsung Electronics is the current market leader.
But on smartphones, the most profitable part of the industry, Microsoft will continue to lag far behind rivals. Apple and devices running Google's Android operating system accounted for about 96 percent of the 290 million smartphones shipped in the fourth quarter, according to IDC. Devices using Microsoft's Windows Phone software had an estimated three percent.
Microsoft's new chief executive, Satya Nadella, got off to a winning start with Wall Street as the company eased past analysts' profit estimates, despite the pressure of falling computer sales.
It reported quarterly profit of US$5.66 billion, down from $6.05 billion in the year-ago quarter. But that was better than analysts and investors had expected..
Windows PC sales fell 4.4 percent in the quarter, according to the two major technology research firms, making this the eighth straight quarter of declines as tablets and smartphones gain popularity.
Microsoft shares rose almost three percent in after-hours trading to US$40.96, keeping the stock at levels not seen since the turn-of-the-century Internet stock boom.
Investors are banking on Nadella's focus on mobile and cloud-based computing taking Microsoft beyond its traditional PC-based Windows business.
"This quarter is a nice step in the right direction for Nadella and Microsoft," said Daniel Ives, an analyst at FBR Capital Markets.
"We would characterise these results as solid in a choppy IT spending environment," he added.
Ives said Nadella's emphasis on cloud computing helped its server software business, while a softer-than-expected decline in PC sales limited damage to the bottom line.