Former France worldwide scrum-half Fabian Galthie has already been announced as Toulon's new coach for next season.
But after the three-time European champions were knocked out of the Champions Cup in the quarter-finals by Clermont on Sunday, Toulon have chose to bring forward his departure.
After being initially recruited as an assistant coach, Ford took over from Diego Dominguez in October a year ago following the club's poor start to the season. He took over from Diego Dominguez in October, just a month after outspoken club president Mourad Boudjellal had brought the former England defence coach in as Toulon's backs coach.
Matt Giteau will end his six-year stint with Toulon as the French club's backs coach following the departure of Mike Ford.
Ford was due to continue as head coach until the end of the season when former France captain Fabien Galthie will take over, but instead he has paid an immediate price for the club's Champions Cup exit.
Marc Dal Maso will assist Cockerill, with former Australia worldwide Matt Giteau taking up a player-coach role.
Dal Maso will be one of Galthie's assistants next season alongside Fabrice Landreau, Toulon announced last month.
The former Bath Rugby coach was only appointed head coach of Toulon in October of 2016.
Toulon have struggled since Bernard Laporte left the club last summer after leading them to three consecutive European titles from 2013-15.