McCormack, 40, who led the club to the Championship One title in his first season in 2011, wants to spend more time with his family. His father Jim passed away last month.
"The last few months have been a difficult time for my family and I feel as though it is important to take some time out of the game and spend some time with them," he said.
"I would like to place on record my thanks to everyone concerned with the club, especially the fantastic supporters."
In a statement, Swinton said: "The club totally accept Steve's decision and will be ever grateful for his major contribution to our recent success in winning Championship One and avoiding relegation in the Championship in 2012.
"The club will make an announcement about the replacement as soon as all the options have been evaluated."
McCormack, 40, became the youngest coach in Super League when he took charge of Salford at the age of 28 and also had spells at Widnes, Gateshead, Whitehaven and Barrow before joining the Lions.
He will continue as Scotland head coach for this year's World Cup.