Tenet's resignation takes effect in mid-July, after which Deputy Director John McLaughlin will become the agency's acting chief, Bush told reporters at the White House.
Bush said that Tenet informed him of his decision Wednesday night.
Bush said Tenet had done "a superb job for the American people."
"He has been a strong and able leader at the agency," Bush said.
"He has been a strong leader in the war on terror and I will miss him."
He had faced heavy criticism over the September 11, 2001, attacks on New York and Washington, and on the war in Iraq, in which pre-invasion U.S. estimates that Iraq was amassing stockpiles of weapons of mass destruction now appear to have been incorrect.