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.
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“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.
Australia and New Zealand have both followed the US lead and banned Huawei from roles in their respective 5G rollouts.