The Nets announced the news Sunday on Twitter.
According to the New York Post, the Nets gave Bargnani the veteran's minimum ($1.4 million) for the upcoming season, and the contract includes a player option for a second season.
Bargnani, 29, missed most of the past season due to calf and hamstring injuries, playing just 29 games (22 starts). He averaged 14.8 points and 4.4 rebounds in his second season with New York.
Bargnani was the No. 1 overall pick in 2006 by the Raptors. He spent seven seasons in Toronto before the Knicks acquired him ahead of the 2013-14 season in exchange for center Marcus Camby, forwards Steve Novak and Quentin Richardson, a 2016 first-round draft pick and two second-round picks.
In 504 career NBA games (377 starts), Bargnani is averaging 15 points and 4.8 rebounds. His best scoring season was 2010-11, when he contributed 21.4 points per game to the Raptors.