Sprint said in a joint statement with SoftBank that the firms expect to close the merger after the close of trading Wednesday in New York.
A separate deal which gives Sprint full control of the wireless broadband provider Clearwire will close on Tuesday, the companies said.
With the new cash infusion and Clearwire's spectrum, the new Sprint is expected to be able to better compete with the top US carriers, AT&T and Verizon.
SoftBank had targeted Sprint as a way to gain entry into the hot US telecom market. But the Japanese company's efforts ran into competition from Dish Network, which forced SoftBank to increase its offer by $1.6 billion from the original $20 billion proposal.
The deal is the largest overseas acquisition ever by a Japanese firm. Sprint stockholders will retain a 22 percent stake in the new firm.
The SoftBank deal received clearance from US national security officials in May under the condition of appointing an independent member to the Sprint board of directors to serve as security director.
The director, who must be approved by US authorities, would oversee national security matters and serve as a point of contact for US agencies.
The Federal Communications Commission gave final US regulatory approval to the deal on Friday.