Tortorella led the Tampa Bay Lightning to the Stanley Cup title in 2004 and was let go following last season. The Rangers were not required to provide compensation to the Lightning.
Renney, a former coach of the Vancouver Canucks, was 164-121-42 with the Rangers in four-plus seasons and ranks fourth on the team's career wins and games coached lists.
In recent home games, fans had chanted for Renney's dismissal.
"I've been thinking about it the last couple of weeks," general manager Glen Sather said. "I wish it hadn't have come to this, but it did. After the last two or three games it was obvious something had to be done."
Assistant coach Perry Pearn was also fired, but fellow assistant Mike Pelino was retained along with goalie coach Benoit Allaire, the Rangers said. Jim Schoenfeld, the team's assistant general manager, will also serve as an interim assistant coach.
Schoenfeld wasn't considered to replace Renney, but Sather said Tortorella wasn't the only candidate he spoke to Monday. Sather declined to reveal specific terms of Tortorella's contract, but said it was a multiyear deal. Tortorella was expected to conduct practice Tuesday morning.
Tortorella was a Rangers assistant coach, before joining the Lightning, and went 0-4 as an interim New York head coach after replacing John Muckler at the end of the 1999-2000 season.
His no-nonsense style is in stark contrast to the laid-back, player-friendly Renney. That was a key factor in Sather's decision to hire him. Tortorella got the job less than 10 hours after it became available.
"Torts is going to bring a lot more fire to his approach," Sather said. "I just felt that we needed to get more fire in there."
Renney stated strongly Sunday that his team hadn't quit and played hard despite its 3-2 overtime loss to Toronto that extended New York's skid to 2-7-3. The Rangers face the Maple Leafs again in Toronto on Wednesday. Sather said the decision to change coaches was made before the latest defeat.
The players met with Renney and Sather following a Monday morning workout at the team's suburban practice facility. Sather said Renney took the news in a professional fashion.
"Sometimes you have to accept that you need a change and you have to do it," goalie Henrik Lundqvist said. "It's all about winning, and someone had to pay the price. But we're all responsible for this."
The Rangers (31-23-7) entered Monday in a fifth-place tie in the Eastern Conference, but only two points above ninth-place Carolina.
The top eight teams make the playoffs.
Renney is the second Atlantic Division coach fired in the past week, following Pittsburgh's dismissal of Michel Therrien last weekend - a move also made one day after a loss to Toronto. Renney is the sixth NHL coach let go this season, which includes all four coaches whose teams started the regular season in Europe.
Renney went 2-0 against former Lightning coach Barry Melrose in games in Prague. Therrien and the Penguins faced Craig Hartsburg and the Ottawa Senators in Stockholm.
After a two-season stint as the Rangers director of player personnel, Renney became an assistant coach under Sather for the 2003-04 season. Sather relinquished his coaching duties Feb. 25, 2004, and turned the team over to Renney on an interim basis.
The defensive-minded Renney, who turns 54 on Sunday, went 5-15 to finish that season and took over on a full-time basis in July 2004, but had to wait for the yearlong NHL lockout to end before he could officially claim the job behind the bench.
In his first full season, Renney was a finalist for the Jack Adams award as coach of the year after the Rangers went 44-26-12 and reached the playoffs for the first time since 1997. They advanced to the second round each of the past two years.
Sather turned over the roster before this season, allowing veteran forwards and proven goal scorers Jaromir Jagr and Brendan Shanahan to leave via free agency along with the volatile Sean Avery.
Markus Naslund was brought in, and he leads the offensively challenged Rangers with 18 goals. The biggest disappointment has been the signing of defenseman Wade Redden, who was given a six-year, $39 million deal, but now hears boos every time he touches the puck at home.
New York ranks 29th of 30 teams in goals per game (2.33) and has scored two or fewer 14 times in 19 games - including their past 12 losses.
Renney also struggled to get the most out of centers Scott Gomez and captain Chris Drury, who signed as free agents in the summer of 2007 but never found consistent linemates to work with.
"It's a tough part of the business," Gomez said. "As players, it's definitely on us. We feel 100 percent responsible, but also, we still have a lot of games left and we're still in position where we can get into the playoffs. We have to find it. We have to find a way."