The contract includes a team option on the second year, the source said.
Barbosa weighed in on his move via Twitter.
Barbosa, 33, joined the Golden State Warriors in 2014 after a brief second stint with the Suns, which came after he played a season in his native Brazil for Esporte Clube Pinheiros. A 13-year veteran, he averaged 6.4 points and 1.2 assists in 68 games last season.
Known as the "Brazilian Blur" because of his quickness, Barbosa showed flashes of his former athleticism in the NBA Finals, scoring 11 big points off the bench in Game 1 against the Cleveland Cavaliers.
Information from ESPN staff writer Royce Young was used in this report.