Prior to playing professionally, Adams competed on travel teams and for Grandview Preparatory School in Boca Raton, Florida.

Adams played in amateur baseball tournaments from a young age, winning the championship in a 12-and-under travel competition for a team representing Broward and Palm Beach counties, against a team representing California's Central Valley, at the Baseball Hall of Fame in Cooperstown, New York.

[5] Baseball America rated Adams as the second-best high school third baseman in the United States.

[6] The Detroit Tigers chose Adams in the 21st round of the 2005 Major League Baseball Draft, but, disappointed with where he was selected,[7] he opted not to sign, instead enrolling at Virginia.

As a sophomore, in 2007, he had a .372 batting average and a .454 on-base percentage, earning Second-Team All-Atlantic Coast Conference honors.

[9] Out of Virginia, the New York Yankees selected Adams in the third round (106th overall) of the 2008 Major League Baseball draft.

When the teams shared medical reports, the Mariners determined that Adams' ankle was broken, not sprained.

[18][16] Still rehabilitating from his ankle injury, Adams played for Tampa and the Rookie-level Gulf Coast Yankees in 2011.

[20] Adams spent the 2012 season with the Trenton Thunder of the Double–A Eastern League, where he hit .306/.385/.450 over 383 plate appearances.

[24] After playing in 27 games for the Scranton/Wilkes-Barre RailRiders of the Triple–A International League, in which he batted .316,[9] the Yankees purchased his contract on May 15, the first day he was eligible to be promoted to the majors.

On May 20, Adams hit his first major league home run off Freddy García in a game against the Baltimore Orioles.

[42] On November 23, 2015, Adams signed a minor league contract with the Toronto Blue Jays that includes an invitation to spring training.

[44] In the offseason, Adams played 16 games for the Tigres de Aragua of the Venezuelan Professional Baseball League.