A separate statement by the Cuban and Norwegian embassies in Bogota said the rebels turned the 26-year-old over to a commission made up of representatives from their countries and the International Committee of the Red Cross in the nation's south.
Sutay was later delivered to US government representatives at the airport in the Colombian capital, Al Jazeera reported.
"We welcome the release today of Kevin Scott Sutay from captivity at the hands of the FARC," the State Department said in a statement on Sunday.
"The United States is profoundly grateful to the Government of Colombia and commends its tireless efforts to secure his release. We offer special thanks to President Juan Manuel Santos for his assistance."
Sutay, a veteran of the war in Afghanistan, had been backpacking through several Central and South American countries before he was captured by the FARC.
He had been warned by police to abandon his plans to hike through what they called a "red zone" for rebel activity and was held for more than four months.
The FARC showed willingness to release Sutay in July but hardened its stance, accusing him of being a mercenary, soon after Santos refused to allow a high profile left-wing politician to oversee the liberation.
The FARC and their smaller counterpart, the ELN, have been fighting the government in a bloody five-decade conflict that has killed more than 200,000. Both are listed as 'terrorist' organisations by the United States and European Union.