Cockerill, 46, was sacked by Tigers on Monday after nearly eight years in charge of the Premiership club.
He will work under ex-Bath head coach Mike Ford, who took over at three-time European Champions Toulon in October.
Leicester won three Premiership titles under Cockerill, and finished runners-up on two other occasions.
Former Leicester director of rugby Richard Cockerill has joined French side Toulon as a rugby consultant until the end of the Top 14 season in May.