Bogosian, 23, will carry an annual salary-cap charge of $5.143 million. The Jets have been active in the offseason, locking up forward Blake Wheeler on a six-year, $33.6 million contract last week.
Bogosian played in 33 games and had 14 points on five goals and nine assists last season and had 30 points in 65 games with the Jets in 2011-12.
He has appeared in 297 games for the Jets starting with three seasons in Atlanta, and has 103 points on 34 goals and 69 assists.
The Atlanta Thrashers, the franchise's prior location and moniker, made Bogosian the No. 3 pick in the 2008 NHL Draft. HACKEL: Maple Leafs attract attention for odd reasons