FCC approval was the final hurdle for the telecom deals.
Republican FCC Commissioner Ajit Pai negotiated to remove wording in the final order related to the way the FCC calculates spectrum holdings, according to the people familiar with the proceeding.
SoftBank will pay $21.6 billion to own 78 percent of Sprint.
Dish Network had pushed its own competing proposals for both Sprint and Clearwire, forcing SoftBank to raise its offer, but the satellite TV company abandoned its bids last month.
Dish had warned that allowing SoftBank to own such large U.S. telecommunications networks would pose a threat to national security. Sens. Charles Schumer (D-N.Y.) and John McCain (R-Ariz.) also expressed concern about the SoftBank deal.
To allay security concerns, SoftBank agreed to give the U.S. government veto power over the appointment of one Sprint board member, who will oversee national security issues for the company. Sprint has said it will appoint Retired Adm. Mike Mullen, the former chairman of the Joint Chiefs of Staff, to the post.
The U.S. government will also be able to review and approve contracts with certain network equipment makers.
After SoftBank agreed to those conditions, an interagency panel cleared the deal of security concerns in May.
—Updated at 5:29 p.m.