The announcement came a day after Andrews' wife, Camille, withdrew her name as a candidate for the seat. She won a primary in his South Jersey district on the same day that her husband lost to Sen. Frank Lautenberg in the Democratic Senate primary.
Andrews told The New York Times his wife intended to be a "serious candidate," not a place marker for her husband.
"I had no intention of going back to the Congress until a week ago," he said. "I just looked deep into what I believe in and decided that this is what I had to do."
Andrews must be approved by local Democratic leaders by Sept. 17. That vote is considered a formality.
Elsewhere in the state, the decision got mixed reviews. He angered many Democrats when he decided to challenge Lautenberg.
"I guess nothing should surprise me," said Rep. Bill Pascrell Jr., who represents a North Jersey district centered in Paterson. "But obviously it's a flaw in his character. We all have flaws in our character, but we try to solve them. I think it's very disingenuous."