U.S. Defense Secretary Robert Gates presided over the ceremony, traveling unannounced to Iraq for the event and to visit with Iraqi military and governmental leaders, The New York Times reported.
Petraeus will assume command of U.S. forces across the Middle East and Southwest Asia.
During a dinner Monday, Gates presented Petraeus with the Defense Distinguished Service Medal and presented U.S. Ambassador to Iraq Ryan Crocker with the Department of Defense Medal for Distinguished Civilian Service, the Pentagon's highest honor for a civilian, the Times said.
Commenting on the Iraqis' assumption of security duties, Petraeus said U.S. combat troops "are by and large already out of the populated areas in 13 or 14 of Iraq's 18 provinces," adding security duties in 11 provinces were under Iraqi control and another two were "expected to shift in the month of October."
At least three explosions in which at least 32 people died coincided with Gates's visit. One blast occurred at a Ramadan feast in Diyala province and two happened in central Baghdad.
Notable deaths of 2014 [PHOTOS]