"I have enjoyed my four years and eight months at The Hawthorns and I hope the club goes on to bigger and better things," said Burrows.
Burrows was assistant to the last manager, Gary Megson, and for two matches was in charge of the first team before Robson came in.
Alan Cork has been linked with the managers job at MK Dons. Coach Jimmy Gilligan (a former City player) is in caretaker charge at the moment.