The move comes one week after Jones signed a one-year extension with the Roughriders, taking him through the 2020 season.
However, the deal reportedly contained an out clause if Jones landed an NFL job.
"We are proud of what Chris came in and accomplished through his three seasons as general manager and head coach,'' Riders president and CEO Craig Reynolds said in a statement. "His work obviously didn't go unnoticed and we congratulate him on his opportunity in the National Football League and thank him for his contribution to the Saskatchewan Roughriders.''
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New Browns head coach Freddie Kitchens does have a connection with Jones. The latter was a graduate assistant with the Alabama Crimson Tide during Kitchens's final year as a quarterback with the NCAA team in 1997.
Jones, a 51-year-old native of South Pittsburgh, Tenn., joined the Roughriders in December 2015, one week after guiding the Edmonton Eskimos to the Grey Cup as head coach.
The Riders steadily improved under Jones, registering five, 10 and 12 regular-season wins in each of his three seasons with the franchise. He was named CFL coach of the year in 2018 after a 12-6 season, but the Roughriders lost the West Division semifinal against the visiting Winnipeg Blue Bombers.
Jones came to the CFL in 2002, taking a job as defensive line coach of the Montreal Alouettes. He moved up to defensive co-ordinator the following year and stayed in that role until taking the same job with the Calgary Stampeders in 2008.
The Toronto Argonauts hired Jones as defensive co-ordinator and assistant head coach in 2012. He stayed there for two years before becoming head coach of the Eskimos in 2014.
Jones has won four Grey Cups as a coach.
The Roughriders did sign assistant vice-president of football operations Jeremy O'Day through 2020 earlier this month. Paul Jones joined the organization as the assistant GM with a two-year deal while director of football administration Mike Davis and football operations co-ordinator Jordan Greenly also both return.
"We are fortunate to have many quality football leaders and coaches on our staff,'' Reynolds said. "We will evaluate and will look to fill the vacancy quickly.''
(RP.com Wire Services)