Maya was given his jersey and hat and was accompanied by agent/interpreter Bart Hernandez, Nationals general manager Mike Rizzo and pitcher Livan Hernandez.
Maya agreed to play for the Nationals last week, but the deal could not be finalized until he passed a physical, after being granted a visa to enter the United States.
Rizzo said it was the team's "first major international signing."
"We were very aggressive out of the shoot with Maya," Rizzo said. "We thought he could have an instant impact at the Major League level for the long-term."
Rizzo said Maya would be in Washington for a couple of days before going to Viera, Fla., to throw in front of pitching coordinator Spin Williams. Maya will then throw a live bullpen session, a simulated game and a rehab start before re-assessed as to where to go next.
Maya earned Cuba's equivalent of the Cy Young Award during his final season with Pinar Del Rio Vegueros. During that time, he went 13-4 with a 2.22 ERA and tossed seven compete games. Maya went 48-29 with a 2.15 ERA in six seasons with Pinar Del Rio Vegueros.
The right-hander also pitched for Cuba in the 2006 and '09 World Baseball Classic. In six games, he went 1-1 with a 0.87 ERA.
"I'm very happy to be here," Maya said through Bart Hernandez. "I'm going to go out there and do my best. Pretty soon, I hope to be helping the team go forward and I'll do my best here."
Maya described himself as a pitcher who pounds the strike zone, is aggressive and hits the corner with good command.
Livan Hernandez said he met Maya when he was 10 years old and working as a bat boy for a team Hernandez was playing on in Cuba.
Hernandez said he was glad to have another Cuban player added to the Nationals.
"I'm very happy for him," Hernandez said. "It's a dream come true. We got him over here in a free country with the best baseball in the world."