The 2-1 loss to Burnley on Saturday was a club record eighth straight league defeat and they are bottom of the table, 10 points from safety with six matches remaining.
Assistant head coach John Carver has also left the club.
"The Club would like to thank Alan and John for their efforts and wish them well in their future endeavours," read a West Brom statement.
First-team coach Darren Moore will take charge until further notice.
West Brom's next match is at home to Swansea City next Saturday.