The deal includes a purchase of $8 billion in freshly released Sprint stock at a purchase price of $5.25 per share, The New York Times reported Monday.
The additional $12.1 billion will be generated by a purchase of existing shares with SoftBank agreeing to a price of $7.30 per share, which offers shareholders a premium on their holdings.
Sprint shares have been on the rise since Thursday, when it became known that the two companies were discussing a major purchase.
Regulators could block the deal, as could Sprint Nextel shareholders.
Part of the motivation for the deal is cash. Sprint Nextel has been spending billions to upgrade its system to accommodate the huge amount of data that is required to compete in the age of the smart phone.
The company's competition in the United States is Verizon Wireless and AT&T, both of which are about twice as big as Sprint in terms of subscriptions.
Sprint, on the other hand, lost subscribers in droves after its 2005 merger with Nextel.
But much of the business now pivots on the smart phone and for several years AT&T had an exclusive deal with Apple which tied iPhone sales to AT&T subscriptions. That exclusive deal no longer exists, however, and Sprint was able to offer the iPhone as of last year.
The Times said the other reason Sprint Nextel was looking for a cash injection was its enormous debt. The company has about $21 billion in debt, the Times said.
And some of that debt is scheduled to mature in 2013.