The boat capsized after setting off for Europe from neighboring Libya. Survivors told the Tunisian coast guard last week that it had been carrying 86 people.
Tunisian fishermen rescued four people but one later died in hospital, the U.N. refugee agency UNHCR said last week.
“After a week of searches, all the 82 bodies who were in the boat that sank last week were recovered,” Mongi Slim, an official of the Tunisian Red Crescent, told Reuters.
Libya’s west coast is a main departure point for African migrants hoping to reach Europe, though numbers have dropped because of an Italian-led effort to disrupt smuggling networks and support Libya’s coast guard.
Sixty-five migrants heading for Europe from Libya drowned in May when their boat capsized off Tunisia.