The Thrashers will get prospect Ivan Vishnevskiy as well as a fourth-round draft pick in exchange. The 21-year-old Russian defenseman was the Stars' first-round pick, 27th overall, in the 2006 NHL entry draft.
The deal was first reported by ESPN.com's Pierre LeBrun.
Lehtonen will take a physical for the Stars on Wednesday.
"We get a goaltender. That gives us three now, so that's a situation that we'll have to deal with," Dallas coach Marc Crawford said after the Stars lost 4-3 in a shootout to the Chicago Blackhawks on Monday night.
"We've got to make considerations because our other two guys are both free agents at the end of the year," Crawford said.
"Obviously I think they feel pretty good about Kari Lehtonen. He's come back and I've heard that he's played well at the American League level, so we'll see what happens from there on our side."
Turco is slated for unrestricted free agency July 1.
The 26-year-old Lehtonen has not appeared in an NHL game this season, recently recovering from a pair of offseason back surgeries and completing a two-week conditioning stint with Chicago of the AHL. His last NHL game was last April with the Thrashers. He was the second overall pick in the 2002 NHL entry draft by Atlanta but a myriad of injuries has so far derailed his career. The Helsinki native has appeared in 204 career NHL games and sports a .912 save percentage and 2.87 goals-against average.
"He was drafted second overall for a reason, and he's an elite goaltender when healthy," Nieuwendyk said. "Now that he's on the right path, we're going to get a guy that's about to enter the prime of his career."
Pierre LeBrun covers the NHL for ESPN.com. ESPNDallas.com's Richard Durrett and The Associated Press contributed to this report.