WASHINGTON (Reuters) - The last U.S. combat troops in Iraq were crossing the border into Kuwait, more than seven years after a U.S.-led invasion toppled Iraqi dictator Saddam Hussein, NBC News reported on Wednesday.An NBC reporter travelling with the convoy said the troops from the 4th Stryker Brigade would drive through the night on the way to Kuwait."As soon as all these soldiers leave Iraq, Operation Iraqi Freedom, the combat mission in Iraq, will be over," NBC reported.The United States is on schedule to draw down its forces in Iraq to 50,000 by August 31. NBC said the soldiers staying behind would be on a training mission.There are currently about 55,000 U.S. troops in Iraq, down from about 140,000 when President Barack Obama took office in January 2009.As of Wednesday, the Defence Department said there were 4,419 U.S. military deaths since the Iraq invasion.As a presidential candidate, Obama campaigned to end the war responsibly, and as president he has been explicit in his assurances to Americans that not a single U.S. service member will remain in Iraq come January 1, 2012.While violence has dipped sharply since the height of sectarian warfare from 2006-2007, Iraq is still extremely fragile and its leaders have not resolved a number of politically explosive issues that could easily trigger renewed fighting.The war in Iraq has gone on longer than the U.S. Civil War, the U.S. involvement in World War One, and longer than World War Two. Opinion polls show Americans are tired of nearly a decade of war in Afghanistan and Iraq.