The bodies were found by coastguards sent to the scene in the early hours of Monday morning.
Hopes are fading as the search continues for the two other crew members.
Rescue teams began their search for the Flamingo, a 24ft Belgian vessel from Zeebrugge, after Thames Coastguard were alerted by an emergency radio beacon signal at midnight on Sunday.
At about 0145 BST, crew aboard another fishing boat, the Aquarius, sent a mayday message saying the Flamingo had capsized 20 miles east-south-east of Harwich and they could see the boat's keel.
The bodies of two men were found within a mile of the trawler in sea conditions described as "relatively good" with force two to three winds.
A Royal Navy diving team from Portsmouth has been searching for possible survivors trapped underneath the upturned boat.
A Belgian rescue helicopter has joined the air search with a Sea King helicopter scrambled earlier from RAF Wattisham.
Harwich and Walton-on-the-Naze lifeboats are also involved in the search.
Stewart Oxley, of the Walton lifeboat station, said the sea conditions were not too bad when they received the emergency call.
"Daylight makes the job a lot easier but one thing we're all hoping is that we find survivors.
"At the moment a rigorous search is being undertaken, co-ordinated by the coastguards.
"They'll be working from a position where the vessel was first sighted and then taking into account the tides, and spreading out from the position to find what wreckage and what people we can."