"Shiv is a legend of the game and has been an outstanding influence on and off the field for Derbyshire," elite performance director Graeme Welch said.
"It's been a privilege to have him and he has played a central role in some important recent wins in 50-over and four day cricket.
"This is exactly why we moved to bring an experienced overseas alternative to the club in Marcus North, who is already with the squad and up to speed with the conditions."
The former Durham, Lancashire and Warwickshire batsman has been with Derbyshire for the past two seasons, scoring 1,471 runs in 23 first-class matches, and 495 runs in limited-overs competitions.
He scored 52 against Leicestershire in the club's One-Day Cup opener on Sunday in his final innings of the season.
West Indies will play three one-day internationals a T20 game and two Tests against Bangladesh between 20 August and 17 September.
Shiv has left all the money in England to come and represent West Indies against a minnow team in Bangladesh. He is dedicated to WI cricket a lot more than certain players and yet still he his being given a fight to retire.