Ford, 51, had been given the job last October but failed to make an impact as Toulon were knocked out of the Champions Cup quarter-finals by Clermont last weekend.
Cockerill, who joined Toulon as assistant coach in January, will be assisted by former France hooker Marc dal Maso with Australian Matt Giteau coaching the three-quarters while continuing to play for the first team.
Toulon said last month that former France scrumhalf and captain Fabien Galthie would take over as manager next season.
Toulon have struggled since Bernard Laporte left the club last summer after leading them to three consecutive European titles from 2013-15.
Laporte was replaced by Diego Dominguez but the Argentine was sacked after just a few weeks, with Ford taking over.
The former Bath boss fared little better than Dominguez, however, and he leaves Toulon fourth in the Top 14, 23 points behind runaway leaders La Rochelle, and only five points above 10th-placed Toulouse.
His one-year contract had an option for an additional season but Toulon had already said both parties had agreed not to take it up.
(Reporting by Julien Pretot; Editing by Peter Rutherford)
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