The 21-year-old defenceman signed a US$5-million, two-year deal with the team on Wednesday.
Bogosian was a restricted free agent who waited all summer to get a new contract.
He arrived in Winnipeg earlier this week to participate in informal workouts with his teammates and told reporters he was anxious to officially join the Jets.
In 199 career NHL games for the Atlanta Thrashers, Bogosian had 24 goals and 59 points.
He was the third overall pick in the 2008 draft.