The Canadiens also sent a conditional 2013 fifth-round pick in exchange for Blake Geoffrion, minor league forward Robert Slaney and a 2012 second-round pick in 2012.
Geoffrion, the 23-year-old grandson of Canadiens legend Bernie (Boom Boom) Geoffrion, appeared in 22 games for Nashville this season and had three assists.
"Wow..what a day...it's bitter-sweet, going to miss my hometown of Nashville, but going to where it all started with my family...MONTREAL!!!" he wrote on Twitter.
The Predators will receive the conditional pick only if Geoffrion plays at least 40 games in Montreal next season.
"If it wasn't for Montreal, the unique situation with his family, the history, all that stuff, I probably wouldn't have traded him," Predators general manager David Poile said on a conference call. "It's extremely tough to do because of his obvious ties to Nashville.
"It was fabulous to have a local player here in Nashville."
Gill, a Stanley Cup winner with Pittsburgh in 2009, is slated for unrestricted free agency July 1.
"We needed a veteran defenseman with experience and size," Poile said. "I think that in Hal Gill, we get everything we were looking for."
Gill, 36, has played in 1,047 regular-season games in 15 seasons, plus 105 playoff games.
Gill, 6-foot-7 and 240 pounds, has a goal and seven assists and 29 penalty minutes this season, his third season with the Canadiens.
"His leadership and commitment were much appreciated," Canadiens general manager Pierre Gauthier said in a statement.
Information from The Associated Press was used in this report.