The all-stock deal would see the companies – third and fourth-largest in the US telecoms industry – combine to serve 127 million customers and employ more than 200,000 people.
The agreement is likely to attract regulatory scrutiny, with concerns over competition and fears it could mean higher prices for customers, as a combined company would not have to offer as many promotions to lure new users.
John Legere, president and chief executive of T-Mobile US, said: “This combination will create a fierce competitor with the network scale to deliver more for consumers and businesses in the form of lower prices, more innovation, and a second-to-none network experience – and do it all so much faster than either company could on its own.”
There are also concerns over employment, with The Communications Workers of America union saying the deal will cost at least 20,000 US jobs.
But Mr Legere said on Twitter: “From day one, the new T-Mobile will always have more US employees on payroll than both standalone companies.
“Last year we added 27,000 jobs associated with our growth, and there’s no reason we can’t grow at the same rate.”
Deutsche Telekom currently owns more than 63% of T-Mobile, while Japan’s SoftBank owns 84.7% of Sprint.
The new larger business would be 42% owned by the German company, which would also nominate nine of the board’s 14 directors.
SoftBank would nominate four directors and own 27% of the company.
It is not the first time Sprint and T-Mobile have tried to merge.
Talks in 2014 failed because of regulatory opposition from the Obama administration, and last year because of disagreements over who would control the combined company.
Analysts greeted the news with mixed feelings.
BTIG Research analyst Walter Piecyk raised concern over Sprint’s debt and annual losses, saying that, while it had cut costs, it had not invested enough in its network.
He added: “T-Mobile does not need a merger with Sprint to succeed, but Sprint might need one to survive.”
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But MoffettNathanson analyst Craig Moffett said T-Mobile’s momentum was slowing, which may explain why the company and its German parent “have warmed to the idea of a merger sooner rather than later”.
The company, which would be called T-Mobile, will have headquarters in Bellevue, Washington (T-Mobile’s current base) and Overland Park, Kansas, Sprint’s home.