The infielder made his major-league debut Wednesday night, starting at third base and batting sixth against the Seattle Mariners on his 26th birthday.
Adams is expected to receive the majority of the starts at third base until Kevin Youkilis returns to the lineup. The infielder can also play second or first base if necessary, but is not considered a strong defender.
The right-handed hitting Adams has swung the bat well this year in Triple-A, hitting .316/.407/.490 in his first 113 plate appearances. Adams also had a successful offensive season in 2012, posting a .306/.385/.450 triple slash.
The Yankees actually released Adams earlier this season after the infielder missed most of spring training with a back injury. The team needed his spot on the 40-man roster after acquiring Vernon Wells. Adams chose to remain with the team, and is being rewarded for his choice.
New York acquired Nelson from the Colorado Rockies on May 3 to give the team some depth at third base. Nelson struggled offensively for both teams, as he hit .235/.269/.304 in 108 plate appearances this season despite a .329 BABIP.