Frye started all 82 games for the Phoenix Suns last season, averaging 11.1 points and 5.1 rebounds in 28.2 minutes per game.
"I'm extremely proud of my time as a Phoenix Sun, but definitely extremely excited to be going to Orlando," Frye told ESPN.com. "Can't wait to embrace the culture and the city of Orlando.
"[The Magic] were very aggressive and made it clear that I was a main target for them," he said. "They want to bring in quality, character guys. They are a young team, but I've been on young teams before. I don't believe anyone who says they're a bad team; they have talent.
"I've been on teams before where we were picked to finish last and we beat all the expectations and did very well. I'm excited to do the same in Orlando."
Last Monday, the Magic added guard Willie Green off waivers from the Los Angeles Clippers and waived longtime point guard Jameer Nelson.
ESPN.com's Amin Elhassan contributed to this report.