Anderson, a performance artist, told The Times of London she's "been spending a lot of time in Cleveland these past few weeks" after Reed's transplant.
It "went very well," she said.
Reed, 71, has a long history of taking drugs, especially heroin, Britain's The Daily Telegraph reported Saturday.
"I take drugs just because, in the 20th century, in a technological age living in the city, there are certain drugs you have to take just to keep yourself normal like a caveman, just to bring yourself up or down," he once said.
Reed stopped using drugs several years ago, but his health has still suffered. He previously underwent treatment for hepatitis, The Daily Telegraph said.
Anderson said she and Reed chose the Mayo Clinic for his surgery instead of a hospital in their hometown of New York because she feels New York's hospitals are dysfunctional.
The Mayo Clinic has "the best results for heart, liver and kidney transplants. Whenever I get discouraged about how stupid technology is and how greedy and stupid Americans are, I go to the Cleveland clinic because the people there are genuinely very kind and very smart," she said.
Anderson said Reed is recovering well and could be back to work in a few months.
"He'll never totally recover from this," though, she said.
2014: The Year in Music [PHOTOS]