Tortorella won a Stanley Cup with the Lightning in the spring of 2004, but was fired in June of 2008 with one year remaining on his contract.
The Rangers, who also dismissed assistant coach Perry Pearn, have lost 10 of their last 12 games, including a 3-2 overtime setback at home against Toronto on Sunday.
New York has a record of 31-23-7 and is currently 10 points behind first-place New Jersey in the Atlantic Division. The Rangers are also sixth in the Eastern Conference playoff race with 69 points, just two ahead of ninth-place Carolina. The top eight teams qualify for the playoffs.
Renney becomes the sixth NHL coach fired this season, joining Chicago's Denis Savard, Tampa Bay's Barry Melrose, Carolina's Peter Laviolette, Ottawa's Craig Hartsburg and Pittsburgh's Michel Therrien. Curiously, all four teams that began the season in Europe -- Tampa Bay, Ottawa, Pittsburgh and the Rangers -- all made coaching changes.
The Rangers opened the season with five straight wins and finished October with a 10-2-1 mark, but have slid considerably since. In the past 12 games, the club has scored more than two goals just twice, and the low point came in a 10-2 setback at Dallas on February 6.
Renney took over behind the Rangers bench in February, 2004 after president and general manager Glen Sather relinquished the duties. The team finished the '03-04 campaign with just five wins in Renney's 20 games, but things turned around after the cancelled 2004-05 season.
The Rangers made the playoffs in each of the three seasons following the resumption of play, winning one series each of the past two springs.
Renney posted a record of 164-121-42 with the Rangers. He was also the head coach in Vancouver for 101 games from the beginning of the 1996-97 season until November of 1997. He had a mark of 39-53-9 with the Canucks.
Tortorella was previously an assistant with the Rangers and took over as interim coach for the final four games of the 1999-2000 season after John Muckler was fired.
After being passed over for the Rangers' full-time job before the 2000-01 season, Tortorella went to Tampa Bay as an associate coach for Steve Ludzik and took over as head coach with 43 games remaining in that campaign. In six- plus seasons with the Lightning, Tortorella guided the club to a record of 239-222-38 with 36 ties.