Last week, Concepcion worked out for the Rangers in front of a contingent that included owner Nolan Ryan at the team's complex in the Dominican Republic. The Rangers, Yankees, Cubs and White Sox had expressed the most interest in signing the left-hander.
The Marlins, Phillies, Giants, Blue Jays, Red Sox and Royals also showed interest.
"Everything is great. I really don't know how to describe it," Concepcion, 18, said by phone from the Dominican Republic last week. "All the training and exercise I have done is paying off. I've worked so hard to get here. I'm so happy. It's like a dream come true."
Concepcion, who was named Rookie of the Year in the Cuban Serie Nacional in 2010-11, after posting a 10-3 record and a 3.36 ERA in 21 games with Industriales de la Habana, defected from Cuba last June during the World Port Tournament in the Netherlands. He later established residency in Mexico, and was declared a free agent last week.
He has been working out in the Dominican Republic and starred in a showcase for Major League scouts on the island earlier in the month.