Sprint said it would pay $2.2bn (£1.4bn) for the stake, but it still needs approval from other shareholders.
The price was lower than had been expected and Clearwire shares fell sharply on Nasdaq.
The deal had been expected since Sprint agreed to be taken over by Japanese mobile operator Softbank in October.
Sprint said the $2.97-a-share offer was 128% above Clearwire's share price the day before the Sprint-Softbank talks were confirmed, and 40% above the price before it made its initial $2.60 a share offer.
As well as already owning half of Clearwire, Sprint is also its biggest customer.
Sprint shares rose 1.8% on the news.
No alternativeSprint said it had already received commitments from holders of 13% of Clearwire shares to vote in favour of the acquisition.
There have been reports that Softbank is not prepared to agree to a price above $2.97 a share.
Some Clearwire shareholders said that last week's $2.90-a-share offer grossly undervalued the company, but the company's chief executive said the board had no alternative.
"Despite our efforts we have been unable to secure new partnerships," said Clearwire chief executive Erik Prusch.
"Our existing governance agreements prevented us from offering third parties the governance rights they desired in a partnership."
