Bryan, who won 16 Grand Slam titles in men's doubles with his twin brother Mike and seven in mixed doubles, will take charge for the group stage in September this year.
He deputised as acting captain last year when Mardy Fish was unable to travel to Scotland after contracting COVID-19.
"I am extremely honoured and humbled for this opportunity to captain the United States Davis Cup team," Bryan said in a statement.
"I have been inspired watching these young American players continue to rise and I am motivated to contribute to this positive momentum.
"I am passionately looking forward to working with the players, their coaches, teams, and the USTA support staff in our mission to bring the Cup back to the United States."
Last month, the United States swept Uzbekistan aside in Tashkent to qualify for the Davis Cup Finals group stage.
Mackenzie McDonald and Tommy Paul had given the Americans a 2-0 lead before the doubles pairing of Austin Krajicek and Rajeev Ram won to give them an unassailable lead.
Denis Kudla then stepped on court for his Davis Cup debut in the third singles rubber to seal a 4-0 victory.
Bryan played for the U.S. Davis Cup team from 2003 to 2020, helping the country win their last trophy in 2007 to extend their record to 32 titles.
The Bryan brothers, who won Olympic gold in 2012, have a 25-5 record in Davis Cup. They retired in 2020.
