Sources told ESPN.com that the Suns have reached a verbal agreement on a four-year deal worth an estimated $34 million that Dragic has pledged to sign July 11, which is the first day contracts can be signed.
Dragic will have a player option entering the fourth year, sources said.
The move capped an extremely busy Wednesday night for the Suns.
Earlier, they agreed to a sign-and-trade deal to send Nash to the
Los Angeles Lakers and, according to ESPN.com sources, struck an agreement on a three-year, $18 million contract with
free agent forward Michael Beasley.
Dragic, who previously backed up Nash in Phoenix and memorably uncorked a 23-point fourth quarter against the San Antonio Spurs in the 2010 playoffs, rose to prominence in the second half of last season with the Houston Rockets following an injury to Kyle Lowry.
But negotiations with the Rockets broke off quickly this week, with Dragic determined to not only secure a deal paying $10 million annually but also the promise of a starting job. The Suns traded Dragic to Houston along with a first-round pick for Aaron Brooks at the 2011 trade deadline.
Dragic has averaged 11.7 points and 5.3 assists in 28 minutes per game in his career, mostly as a backup.
The Slovenian was drafted in the second round in 2008, the 45th pick overall, by San Antonio, then his draft rights were traded to the Suns.
Information from The Associated Press contributed to this report.