The announcement came a day before a scheduled Sprint shareholders' meeting to vote on SoftBank's offer, which faces a challenge from Dish Network's counter offer of $25.5 billion for Sprint, the No. 3 U.S. mobile provider. That meeting has now been adjourned until June 25.
Hedge fund and No. 2 Sprint shareholder Paulson & Co said it would vote all of its shares in favour of SoftBank's improved offer.
(Read More: SoftBank Eyes Merger With T-Mobile as 'Plan B')
SoftBank will increase its cash injection to Sprint shareholders to $4.5 billion, bringing the total cash consideration to $16.5 billion, Sprint said in a separate statement.
Sprint also said its committee evaluating Dish's bid has unanimously determined that it "is not reasonably likely to lead to a 'superior offer'".
"As a consequence of the lack of progress with Dish and the improved terms from SoftBank, the special committee ended its discussions with Dish," Sprint said.
The revised deal with SoftBank gives Dish a June 18 deadline for providing a best and final offer.
Shares of SoftBank were up 0.5 percent on Tuesday morning, in line with a 0.3 percent rise in the benchmark Nikkei average.