The Norwegian-flagged Ocean Viking will "conduct search and rescue activities in the central Mediterranean" for SOS Mediterranee and Doctors Without Borders (known by its initials in French as MSF), the group said in a statement.
"As people are still fleeing Libya on one of the most perilous sea crossings in the world, and with almost no available rescue assets present in the central Mediterranean, it has been an imperative for both SOS Mediterranee and MSF to return at sea following the ending of their operations with the Aquarius in December 2018."
After nearly three years of operations in which it rescued some 30,000 migrants, the Aquarius was forced to cease operations in December 2018 because of what the group said was obstruction by some European countries.
The International Organization for Migration says at least 426 people have died trying to cross the central Mediterranean so far this year.
SOS Mediterranee said the migrants were attempting "to escape the escalating conflict in Libya and the deplorable conditions of Libyan detention centres".
The new operation comes one month after the arrest in Sicily of the German captain of the Sea-Watch 3, Carola Rackete, for docking without permission to land rescued migrants.
Rackete was held for several days after the Sea-Watch 3 hit an Italian police speedboat while entering the port of Lampedusa island despite a ban from entering Italian waters.
She argued she was compelled to avert a human tragedy and bring ashore 40 migrants who had been rescued on June 12 in the Mediterranean.
"For a year now we have been witnessing a deterioration in the European Union’s response in the evolving human tragedy in the central Mediterranean," said the head of operations at SOS Mediterranee, Frederic Penard.
EU states have "continued a harsh campaign of criminalisation against civil society rescue ships and most importantly, there is still no coordinated, sustainable and shared mechanism of disembarkation in accordance with maritime law".
He told AFP said the Ocean Viking would not enter Libyan territorial waters.
"Our presence at sea is to save lives. We hope that the countries will understand and join with us as there is no other solution in the central Mediterranean.
"To say that it's the rescue vessels that are encouraging (migrant) crossing is false. Even without the boats, the departures continue and huge number of a drownings are reported."
Funded in partnership with MSF, the Ocean Viking has 31 people on baord, including 13 search and rescue team members from SOS Mediterranee, nine MSF staff and nine marine crew members.
Libya, which has been wracked by chaos since the 2011 uprising that killed dictator Moamer Kadhafi, has long been a major transit route for migrants, especially from sub-Saharan Africa, desperate to reach Europe.