The contract is for two years with the second year partially guaranteed.
Brown averaged 11 points and 2.7 rebounds in a career-high 23.7 minutes per game last season. He appeared in 59 games, 19 as a starter.
He came to the Suns as a free agent in 2011, signing a one-year deal.
Shooting guard is a position of need for the Suns, who had signed restricted free agent Eric Gordon to a contract but it was matched by New Orleans.
The team has worked out a three-team trade that would send Minnesota guard Wesley Johnson and a first-round draft pick to the Suns.