The decision comes after a stand-off that lasted more than a week.
The Ocean Viking, operated by rescue group SOS Méditerranée, declared a state of emergency on Friday, citing fears for the safety of both migrants and crew.
The migrants are set to be transferred to a government vessel in Sicily on Monday and will quarantine for 14 days.
Medics have already tested those on the Ocean Viking for coronavirus and the results are expected on Monday.
The migrants are from a range of countries including Pakistan, Eritrea and Nigeria.
They had fled the coast of Libya when they were rescued in four separate groups between June 25 and 30.
They include 25 minors, most of whom are unaccompanied by adults, and two women, including one who is pregnant.
The ship had been awaiting permission to allow the passengers off the vessel in either Italy or Malta.
As time went on, those on board had become desperate to reach land - while others, unable to contact friends and family to let them know they were safe, had become distraught, according to reports.
One crew member said there had been a series of fights and threats of suicide.
SOS Méditerranée wrote on Twitter that the “unnecessary delay of this disembarkation has put lives at risk”.
More than 110,000 migrants tried to cross the Mediterranean last year.
More than 1200 died during the attempt, according to the International Organisation for Migration.
It is thought that warmer weather during summer could lead to an increase in the number of attempts.
