"The president has asked me if I would serve again as his running mate. I've agreed to do that," he said Tuesday in an interview with The Dallas Morning News.
The White House confirmed the president has asked Cheney to run with him again, reports CBS News Correspondent Mark Knoller. Spokesman Ari Fleischer called it a "formality."
Cheney's position on the 2004 ticket has been the subject of heightened speculation because of his heart condition. He has had four heart attacks, though none as vice president.
"I've got a doc with me 24 hours a day who watches me very carefully," said Cheney. "If I ran into problems where I felt I couldn't serve, I'd be the first to say so and step down."
More recently, Cheney's value has been questioned because of his connection to a corporate accounting scandal. The Securities and Exchange Commission is investigating accounting practices at Halliburton Co. while Cheney was its chief executive officer.
Cheney, 61, has already said he would relish a chance to join Mr. Bush for any 2004 re-election run. In November, Mr. Bush indicated he wanted his vice president to reprise his role, saying "there's no reason for me to change."
Cheney said he did not know when Mr. Bush would formally announce his candidacy.
Fleischer said the president will have something to say "at the appropriate time."