The ship has been at the center of a standoff between France and Italy last month, when Italy's new far-right government under Prime Minister Giorgia Meloni blocked access to its ports.
At the time, the 230 migrants on board were eventually allowed to disembark in France after spending weeks at sea, thus escalating tensions between the two European nations.
The ship, run by SOS Mediterranee, has been given permission to dock at the port of Ravenna in northeastern Italy, the NGO said, but said it would take "four long days of navigation" to reach it.
The migrants on board were rescued overnight Monday in international waters close to Libya, as the boat carried out its first rescue operation since docking in France.
Among those who had been rescued were 23 women - some pregnant, including around 30 unaccompanied minors, and three babies, according to the NGO. The youngest baby rescued is only three weeks old.
Each year, many migrants fleeing Africa and the Middle East seek to enter Greece, Italy and Spain in hopes of living a much better life within the European Union.
This year alone, the International Organization for Migration (IOM) has recorded nearly 2,000 migrants as dead or missing in the Mediterranean Sea.