“He is grateful to his highly skilled team of doctors and to all who have sent and continue to send their love and support,” the statement said.

A person close to the family says that the surgeon was optimistic after the procedure. Mr. Reid had been quietly letting people know over the past few days that he would be undergoing surgery, including former President Barack Obama.

Mr. Reid was first elected to the Senate in 1986 and became the Democratic leader in 2005. He suffered serious injuries in an exercise accident in 2015, and he did not seek re-election the next year.

On Monday, his successor as Democratic leader, Senator Chuck Schumer of New York, said: “Harry’s a fighter, literally and figuratively. I know he’s going to approach his recovery with the same energy and tenacity and resolve that defined his public life.”

Mr. Reid, known for a biting, acerbic wit and a penchant for partisan pugnacity, told The New York Times in March that he was ready to leave Washington behind. He was selling his apartment in a Ritz-Carlton here and planned to be in the nation’s capital infrequently.