Crowder spent the tail-end of last season as a member of the Miami Heat team that made its way to the NBA Finals.
The 30-year-old averaged 10.5 points and 5.9 rebounds per game with the Heat during the 2019-20 regular season.
Adding Crowder brings wing and forward depth to Phoenix and continues what has been a busy off-season for the Suns, who appear determined to build off their 8-0 performance in the NBA's Orlando bubble.
His signing could indicate that incumbent forward, Dario Saric, will not be re-signed.
Phoenix began the NBA off-season with a blockbuster deal to acquire Chris Paul from the Oklahoma City Thunder.