The boats - nine wooden boats thought to be converted fishing vessels and six large rubber dinghies - were all found drifting around 45 miles off the Libyan coast after issuing distress calls via satellite phone yesterday morning, the coastguard said.
Boats from the Italian, German and Irish navies took part in the rescue operation, which was coordinated in its initial stages by MOAS, a privately-funded rescue operation operating out of Malta in partnership with the Doctors without Borders (MSF) charity.
The exact number of migrants rescued was put at 3,480 by the coastguard and there were no reports of casualties. One Italian navy boat which was ferrying 475 migrants to Sicily reported that it had seven pregnant women amongst its human cargo.
Nearly 1,800 migrants are thought to have drowned attempting to make the crossing since the start of this year, including some 800 in one sinking that was the biggest maritime disaster in the Mediterranean since World War II.
That disaster prompted European governments to significantly increase search and rescue operations between Italy and North Africa but they have been unable to agree on a longer-term strategy to ease the migration crisis which aid workers blame on conflicts that have created more displaced people around the world than at any time since the end of WWII.