TOKYO — In the priciest-ever overseas acquisition for a Japanese company, Softbank Corp. on Monday said that it would buy about 70 percent of Sprint Nextel Corp., giving the US carrier a much-needed cash infusion and boosting its chances to challenge giants Verizon and AT&T.

The $20.1 billion deal links a struggling US mobile company, still trying to build up its high-speed next-generation network, with a Japanese wireless carrier noted for its history of risky — though so far fruitful — acquisitions.