The Federal Communications Commission said that it agreed to the takeover after AT&T made commitments to divest some spectrum and accept other conditions.
The modifications to the deal "will ameliorate the potential public-interest harms and that will help to ensure the achievement of the asserted public-interest benefits," the FCC said in a statement.
AT&T agreed to give up wireless spectrum in some markets to ensure access for some of its rivals.
The big telecom carrier also committed to deploy high-speed access in areas where it is gaining new spectrum and to allow customers of the Cricket brand to keep some low-rate plans and get trade-in credits for their phones when they migrate to the AT&T network.
The deal had been criticized by some consumer groups who said it would reduce competition in the wireless market, noting that Cricket was used by many low-income consumers who lacked the ability to subscribe to one of the major carriers.
John Bergmayer at the activist group Public Knowledge said the deal "highlights the need for new policies that better address the problem of spectrum consolidation."
"The removal of Leap (and its well-known brand Cricket) from the marketplace is troubling because its low-cost, prepaid price plans are particularly attractive to low-income consumers," Bergmayer said in a statement.
"That said, the Commission has ameliorated some of this deal's negative effects."
The news comes amid a campaign by the parent of number three US wireless company Sprint angling to buy the fourth-biggest carrier, T-Mobile.
Masayoshi Son, chairman and chief executive of Japan's SoftBank, which owns Sprint, told an audience in Washington this week he wants to bring a "fight" to the top telecom carriers but needs to have the "scale" to make investments.
AT&T said in a statement it had closed the acquisition and was preparing to launch "the new Cricket," which would be integrated into its network but keep "simple, low-cost rate plans."
The new Cricket will have access to AT&T's high-speed network, and AT&T will expand the brand across the United States.
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