The cash-and-stock deal, which needs regulatory approval, will give AT&T 34 million new customers and lift its annual wireless revenues to around $80 billion from $58.5 billion in 2010.
It will add to AT&T earnings in the third year after the deal closes, the company said, and help it compete with market leader Verizon.
"This transaction represents a major commitment to strengthen and expand critical infrastructure for our nation's future," said Randall Stephenson, AT&T chairman and chief executive.
"It will improve network quality, and it will bring advanced... capabilities to more than 294 million people.
"Mobile broadband networks drive economic opportunity everywhere, and they enable the expanding high-tech ecosystem that includes device makers, cloud and content providers, app developers, customers, and more."
According to data from comScore, AT&T held a 26.6% market share of US mobile subscribers in December 2010, while T-Mobile accounted for 12.2% of the market. Verizon, meanwhile, accounted for 31.3%.
The deal will give AT&T a big boost in its rivalry with Verizon, which recently started selling the Apple iPhone with an end to the AT&T monopoly.
Analysts said the deal also helps AT&T in the so-called 4G sector offering more advanced wireless services.
"AT&T has been under attack for not being able to match the network capacity of larger rival Verizon," said MG Siegler of the technology blog TechCrunch.
"And when they won the majority of the bids for the open spectrum in 2008, Verizon also had a clear path to the future. Now AT&T is taking another path: buying T-Mobile."
Deutsche Telekom's flamboyant former boss Ron Sommer bought Voicestream more than a decade ago at the height of the dotcom boom, re-branding it T-Mobile, but leaving the German firm struggling under a mountain of debt.
For years it was Deutsche Telekom's main growth-driver but in recent years a string of poor results gave rise to speculation that it wanted to put an end to its US adventure.
"This is a very very valuable deal for Deutsche Telekom. This is a good day," chief executive Rene Obermann said. "The proceeds will give us the financial firepower to finance our expansion plans in Europe."
Deutsche Telekom will get $25 billion in cash and $14 billion worth of shares, making the German firm AT&T's biggest minority shareholder with an eight-percent stake and a seat on the board, based on the current share price.
AT&T has the right to increase the portion of the purchase price paid in cash by up to $4.2 billion with a corresponding reduction in the stock component, Deutsche Telekom said.
The cash portion of the purchase price will be financed with new debt and cash on AT&T's balance sheet. AT&T has an 18-month commitment of $20 billion underwritten by JP Morgan.
Forrester Research analyst Charles Golvin said that the deal will mean that high-speed mobile broadband will improve in quality and coverage, including, in the long run, in rural communities.
"The bad news: the cost of that service won't come down nearly as fast as customers would like, since AT&T and Verizon Wireless combined would own nearly three out of every four wireless subscriptions in the US," he said.
"While clearly troublesome for Sprint and other smaller mobile competitors, it's also bad news for cable operators, whose incipient mobility products will suffer in comparison to what AT&T and Verizon can offer."