Cole, 26, son of Newcastle United and Manchester United legend Andy Cole, netted 12 times in 31 appearances for the Steelmen last season, a major part in them securing Scottish Premiership status.
Motherwell boss Graham Alexander had been keen to keep the former Wigan Athletic forward, who now moves on to pastures new with a time which finished fifth in England’s second tier last season.
Cole’s departure comes hot on the heels of Motherwell defender Charles Dunne’s decision not to sign a new deal at Fir Park in favour of joining Premiership rivals St Mirren on a two-year deal.
One of ’Well’s longest serving players, Dunne, 28, joined the Fir Park club in the summer of 2017 and played a key role in the side that reached both domestic cup finals in his first season in Scotland.
Playing 26 times for the Steelmen the following season, injury would then restrict him to just seven appearances in 2019/20, and then was forced to miss the majority of the last season, returning to the bench in the final matches.
But at least gaffer Alexander has been boosted by the fact that youngsters Dean Cornelius and David Devine have both signed new two-year contracts with the club.
The youth academy products, who have both already made first-team appearances, have extended their stays until the summer of 2023.
“We hope both boys take this opportunity to push hard towards getting in our first team,” Alexander said.
“They’re both talented and motivated lads and it’s a big year for them.
“They’re at an age where they have to be competing with the senior pros and I believe they have the right mentality to do that.
“We look forward to helping them with this challenge.”
Cornelius, 20, made his debut for his boyhood club in May 2019 against Livingston.
Central defender Devine made his debut in the same fixture against Livingston in May 2019 and has been involved in a large number of matchday squads since.