Gates also announced that Bush will nominate Army Lt. Gen. Ray Odierno to replace Petraeus in Baghdad.
Central Command oversees the wars in Iraq and in Afghanistan.
If confirmed by the Senate, Petraeus would replace Navy Adm. William Fallon, who abruptly stepped down in March after a magazine reported that he was at odds with Mr. Bush over Iran policy. Fallon said the report, while not true, had become a distraction.
Army Lt. Gen. Ray Odierno, currently commander of the Army's 3rd Corps based in the U.S., finished in February a 15-month tour as the top deputy to Petraeus in Baghdad.
Petraeus, 55, is widely hailed by the Bush administration and members of Congress for developing and implementing a new strategy in Iraq, including the deployment of some 30,000 additional troops, that dramatically improved security.
Central Command, whose headquarters is in the state of Florida, is responsible for U.S. military operations throughout the Middle East, Central Asia and the Horn of Africa.
Fallon relinquished the command March 28 to his top deputy, Army Lt. Gen. Martin Dempsey, and retired from the Navy earlier this month.