Ottavino grew up in Brooklyn, NY after his family moved there from 24 Charles Street in Manhattan when he was young. He graduated from the Berkeley Carroll School in Park Slope, Brooklyn in 2003. During his days at Berkeley he played his summer ball for the Youth Service League. He also played in the local little league, the 78th Precinct, for which his father is now an umpire. He was drafted by Tampa Bay in the 30th round of the MLB Draft in 2003 but did not sign and chose to attend Northeastern University, where he played college baseball for head coach Neil McPhee. In 2005, he was named America East Pitcher of the Year.
Ottavino pitched for Team Italy in the 2009 World Baseball Classic. On May 29, 2010 he made his debut for the Cardinals. Ottavino was removed from the Cardinals' 40-man roster following the 2010 season. Adam was added back on to the Cardinals 40-man roster on November 18, 2011.  On April 3, 2012, the Colorado Rockies claimed Ottavino off of waivers and sent him to their Triple-A affiliate. He was brought back to the majors later that season. Adam currently wears number 0, and is the first and only pitcher in Major League history to have ever done so.
On July 19th, 2014 against the Pittsburgh Pirates, he gave up the tying run after being aggressively harassed by fans. The game was eventually won by the Pirates.