Sather, 60, who is also the team's president and general manager, said he wanted to focus his attention on managerial duties.
"We've got a couple of weeks left before the trading deadline and it'll give me an opportunity to concentrate on the other duties in this job," Sather said.
The Rangers appear to be headed for their seventh straight non-playoff season despite having the highest payroll in the National Hockey League. They have lost 13 of their last 19 games and are 14 points out of the eighth and final playoff spot in the Eastern Conference.
Renney, who coached the Vancouver Canucks in 1996-97, is the 32nd coach of the Rangers.
Sather, a member of the Hockey Hall of Fame, was coach of the Edmonton Oilers on four of their five Stanley Cup championships in the 1980s.