The two sides reached a deal last week. This is the seventh NBA team for the 6-foot-8 Tolliver, an accurate 3-point shooter who could help fill the void left by the departure of Channing Frye.
The two-year contract is worth $6 million, but only $400,000 is guaranteed in the second season.
"Anthony is a great fit for our style of play," general manager Ryan McDonough said in a statement. "His shooting, professionalism and leadership will help us as we try to continue to build a strong foundation going forward."
Tolliver shot a career-high 41 percent from 3-point range for Charlotte last season, averaging 6.1 points and 2.6 rebounds in 64 games.
Tolliver told RealGM last week that signing with the Suns was "a great opportunity for me."
"The Suns are an up-tempo team, and when I was with Golden State I had a similar style. I'm able to produce at a high level and this style compares to that Golden State team. I can play the three as well, but my natural position is four, rebounding, hitting open shots. The Suns made it clear I'm coming to play the four. Phoenix is a great city, a great family city," he told the website.
The Associated Press contributed to this report.