Rouse will remain as a counselor to the president, an elevated position from his former job as senior adviser.
Two senior administration officials confirmed Obama's decision to The Associated Press on condition of anonymity because it has not been announced.
Obama is expected to introduce Daley on Thursday afternoon at the White House.
Although Daley carries the name of a dynastic family of politics in Chicago, which is Obama's hometown, he and the president haven't been personally close. He offers criteria Obama wants: an outsider's perspective, credibility with the business community and experience in navigating divided government.
Daley also wants the job. At 62, the move will thrust him into the heart of national politics just as Obama adapts to a new reality in Washington, with Republicans controlling the House, working to gut his signature health care law and pushing for major cuts in spending.