The moves were part of a continuing rearranging of President Bush's top staff, which included the replacement of Andrew Card as chief of staff with former White House budget chief Joshua Bolten.
Bolten moved into his position last week, putting his right-hand man, Joel Kaplan, in the role of deputy chief of staff for policy.
A little more than a year ago, Rove was promoted to handle most White House policy coordination.
Administrative officials said Rove was giving up that portion of his job to focus on political affairs as the Republicans try to hang on to both houses in the November midterm elections.
If Rove had stayed in the policy position, the president would have had three deputy chiefs of staff: Kaplan, Rove and Joe Hagin, who oversees administrative matters, intelligence and other national security issues, according to the Associated Press.
"Joel Kaplan is a man of great talent, intellect and experience who possesses a deep knowledge of policy and budget processes," Mr. Bush said in a written statement.
McClellan, meanwhile, appeared with President Bush on the South Lawn, saying, "I have given it my all, sir, and I have given you my all, sir, and I will continue to do so as we transition to a new press secretary."
The president praised McClellan for his work. "I thought he handled his assignment with class, integrity. ... It's going to be hard to replace Scott, but nevertheless he made the decision and I accepted it. One of these days, he and I are going to be rocking in chairs in Texas and talking about the good old days."
McClellan, who repeatedly sparred with reporters over Iraq and other intelligence issues since he took the position in 2003, is expected to remain in his post until a new press secretary is named.