The rescue was filmed by the Turkish coastguards. The video shows a rescuer is dropped into the sea and swims over to the man, wearing a lifejacket, holding onto the end of the boat for his life.
The lone migrant jumped off the boat into the sea and was hoisted up to safety by the rescue helicopter.
Elsewhere in the Aegean Sea, Italian coastguards rescued 23 Pakistani migrants off the coast of the Greek island of Kos.
They pulled two small dinghies, packed with migrants, next to the larger coastguard vessel before hauling them onboard.
The International Organization for Migration (IOM) said it estimates over 76,000 migrants and refugees have arrived in Europe by sea through the first six weeks of 2016.
The daily average of nearly 2,000 arrivals is nearly ten times the daily average of a year ago.
France and Germany on Sunday agreed an EU action plan that involves assistance to Greece to control its borders, reinforcing its means to register refugees but also a fight against smugglers and the acceleration of procedures to expel illegal migrants.
It also includes a package for Turkey to help it curb the influx of migrants into Europe.
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