The Suns acquired rights to the quick, sharpshooting 22-year-old left-hander in a draft-day trade with the San Antonio Spurs.
The Suns see the 6-foot-3, 190-pound European as a backup and eventual replacement for 34-year-old Steve Nash.
The NBA team reached a buyout agreement with Dragic's Spanish team TAU Ceramica.
"It's been a lengthy process," Phoenix general manager Steve Kerr said Monday in a Suns news release announcing the signing.
Although Dragic was the 45th overall pick, the Suns considered him second only to No. 1 pick Derrick Rose among point guards in the draft.
In a video shown on YouTube of the Suns headquarters during the draft, Kerr clenched his fist in triumph, then exchanged high-fives with everyone in the room after completing the trade that nabbed Dragic in the second round. The video also shows Dragic in a pre-draft workout for Phoenix. He did not work out for any other NBA team.
The Suns sent San Antonio their second-round pick -- the 48th overall -- along with a 2009 second-round choice and cash. The Spurs used that pick to select forward-guard Malik Hairston of Oregon.
Dragic had been part of the Slovenian national team since 2006. During the 2007 European championships, he played 28 minutes in Slovenia's upset of Tony Parker-led France.
Dragic spent last season with Union Olimpija, helping the team win the Slovenia League championship and the Slovenian Cup. He averaged 9.7 points, 3.1 assists and 1.2 steals in 13 games. He also averaged 12 points, 3.1 assists and 1.7 steals in 28 Adriatic League games.
"When I was a kid, it was my dream to play in the NBA," Dragic told the Arizona Republic after he was drafted. "It was my wish that the Suns pick me."
The Suns, in their first season under coach Terry Porter, hold their media day next Monday, then begin a five-day training camp in Tucson on Tuesday.