The first one arrived at around 06:30 local time, according to reports.
According to Doctors Without Borders, the ships were carrying approximately 630 migrants, including 123 unaccompanied minors, 11 small children and seven pregnant women.
The refugees had been turned away by Italy and Malta and spent a week in rough seas, with many suffering seasickness.
The Spanish government has set up temporary shelters near the dock to provide medical assistance to these refugees.
A total of 2,320 people, including 1,000 Red Cross volunteers, health professionals, police officers, translators and other officials were involved in assisting the refugees.
David Noguera, a member of Doctors Without Borders in Spain, said most of the refugees are stable.
“The refugees on Aquarius are in stable conditions. But among them there are children, pregnant women and some with burn injuries. The doctors will conduct preliminary physical examinations on them shortly after they arrive,” said Noguera.
Noguera said although the Spanish government has a adopted a migrant-friendly stance, its acceptance does not necessarily spell the end of European countries closing their ports to rescue ships.
He said the long lasting refugee crisis has caused tremendous amount of suffering and even deaths, and that the whole of Europe should work together to deal with the situation.
“The refugees have suffered a lot. All we can do is to call on the European governments and the EU to come up with a rational and effective solution that requires concerted efforts. The refugee crisis has been going on for too long and it has caused too much suffering and too many deaths,” added Noguera.