Softbank President Masayoshi Son, left, and Sprint Chief Executive Dan Hesse shake hands today during their joint press conference in Tokyo. Mobile carrier Softbank, based in Tokyo, has reached a deal with Sprint to acquire 70 percent of the U.S. wireless company for $20.1 billion in the largest ever foreign acquisition by a Japanese company.

TOKYO — Softbank has reached a deal to buy 70 percent of U.S. wireless carrier Sprint Nextel for $20.1 billion in the largest ever foreign acquisition by a Japanese company.

The agreement, announced today at a joint news conference in Tokyo by Softbank President Masayoshi Son and Sprint Chief Executive Dan Hesse, will bring together the third biggest mobile carriers of both Japan and the U.S., underlining the growth ambitions of Softbank, which has made a series of acquisitions and investments over the last couple of decades.

It also shows how the strong yen, which is usually seen as a negative for export-reliant Japan, has boosted the overseas purchasing power of Japanese corporations as a stagnant domestic market pushes them to look abroad for growth.

The deal was given a green light by the boards of both companies. It still needs approval from Sprint shareholders and U.S. regulators. Softbank said the transaction is expected to be completed by the middle of next year.

Son said the investment made sense because the U.S. is the world’s biggest market in smartphones, and it was still growing.

The news of the deal, which leaked late last week, had spooked investors worried about such a big investment and sent Softbank shares lower by about a third in recent sessions. Standard & Poor’s had placed Softbank on “credit watch negative,” meaning its credit rating could be downgraded. Shares of Sprint shot up in anticipation of the offer.

Sprint has struggled in recent years to compete with Verizon and AT&T. The company has $21 billion in long-term debt, and has launched a costly network restructuring and signed a long-term contract to buy $15.5 billion worth of iPhones from Apple over four years.

But Son said Sprint has been recovering on its own lately and is now getting cash, thanks to his investment. Son has a record of buying struggling mobile companies and turning them around, including the Japan unit of Vodafone.

Under the agreement with Sprint, $12.1 billion will go to Sprint shareholders and $8 billion will be fresh capital, which will serve to strengthen Sprint’s balance sheet and networks, Son said. Softbank is offering $7.30 a share for the existing shares, about 27 percent above Friday’s closing price of $5.73.