Robinson took over from Mark McGhee in 2017 and achieved considerable success at Fir Park but resigned following the midweek defeat to Kilmarnock.
Motherwell chairman Jim McMahon told the club website: “I thank Stephen for everything he has done for this club. Year after year, he delivered upon or exceeded the targets set for him.
“On the field, that entailed reaching cup finals, achieving a third-place finish and reaching European competition. Those moments will live long in the memory of supporters and will go down in our history."
Keith Lasley has been named interim manager as Motherwell prepare for Saturday's Lanarkshire derby against Hamilton Accies.
