Selected by the Atlanta Thrashers with the No. 3 pick in the 2008 NHL Draft, Bogosian made the club out of training camp that year. When he made his NHL debut Oct. 10, 2008, against the Washington Capitals, he became the youngest player in Thrashers history at 18 years and 87 days.

Bogosian broke his left leg Oct. 28, 2008, in a game against the Philadelphia Flyers and was out until January. He scored his first NHL goal Jan. 17, 2009, against Nashville Predators goaltender Pekka Rinne, and led rookie defensemen with nine goals that season. He followed it up by playing for the United States at the World Championship in 2009.

In 2009-10, Bogosian became the second Thrashers defenseman to reach double digits in goals in a season (Yannick Tremblay was the other) when he had 10 goals and 33 points in 81 games despite playing much of the season with a broken left thumb. He also had 196 hits, a franchise record at the time.

He continued to be productive with 17 points in 2010-11 and 30 points in 2011-12, the first season in Winnipeg for the franchise, which relocated and was renamed the Jets. 

Injuries limited him to 33 games in 2012-13, but Bogosian had a four-game point streak from April 11-20, 2013, and got his 100th NHL point April 16, 2013, against the Tampa Bay Lightning. 

On Feb. 11, 2015, the Jets traded Bogosian to the Buffalo Sabres with Evander Kane and Jason Kasdorf for Tyler Myers, Drew Stafford, Joel Armia, Brendan Lemieux and a 2015 first-round draft pick. Bogosian made his Buffalo debut Feb. 15, 2015, against Philadelphia and led the Sabres in ice time in 17 of his 21 games with them that season.

Bogosian got his 100th NHL assist on Jan. 16, 2016, against the Washington Capitals.