The US Committee on Foreign Investment, the Justice Department, Department of Homeland Security and Defence Department all gave the green light for the two companies to merge, a statement from T-Mobile said.
The four agencies are together known as Team Telecom.
John Legere, chief executive of T-Mobile US, said: "We are pleased to achieve both of these important milestones in the journey to build the New T-Mobile.
“These approvals assure the strong partnership both companies have with the US Government will continue with the New T-Mobile.
"We look forward to continuing our discussions with the remaining regulatory agencies reviewing our transaction to share our story and subsequently achieve similar positive results.”
The go-ahead for the merger of the third and fourth biggest mobile networks in the US was expected after reports that both Deutsche Telekom, the majority owner of T-Mobile, and Sprint's majority owner, Japanese firm SoftBank, had agreed to exclude Chinese telecommunications giant Huawei as a supplier.
The US has banned the use of Huawei equipment in its 5G networks, claiming that the company can be a conduit for spying by Beijing. Huawei has repeatedly denied that it can be forced to indulge in espionage.