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.
(Read More: Proxy Firm Recommends Vote for SoftBank's Sprint Bid)
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.