Fincke was selected by NASA in April 1996 to be an astronaut. He reported to the Johnson Space Center in August 1996. Having completed two years of training and evaluation, he was assigned technical duties in the Astronaut Office Station Operations Branch serving as an International Space Station spacecraft communicator (ISS CAPCOM), a member of the Crew Test Support Team in Russia and as the ISS crew procedures team lead.
In July 1999, Fincke was assigned as backup crewmember for the International Space Station Expedition 4 crew. Additionally he served as a backup for the ISS Expedition 6 crew and is qualified to fly as a left-seat flight engineer (co-pilot) on the Russian Soyuz spacecraft. He was the commander of the second NASA Extreme Environment Mission Operations (NEEMO 2) mission, living and working underwater for 7 days in May 2002.
In 2013, Fincke served as cavenaut into the ESA CAVES training in Sardinia, alongside Soichi Noguchi, Andreas Mogensen, Nikolai Tikhonov, Andrew Feustel and David Saint-Jacq ues.