The Greek-registered Ice Prince, heading for Egypt, sent out an emergency call at 1900 GMT on Sunday after getting into trouble in high winds in the English Channel.
Lifeboat and helicopter crews staged a dramatic rescue to evacuate 20 people from the vessel, which became stranded off the Devon coast, including a man with a broken leg.
Twelve of the crew were airlifted to Portland by a coastguard helicopter and eight others were taken by the Torbay lifeboat to Brixham.
The ship shed most of its load of 5,258 tonnes of sawn timber. Coastguards said they were expecting a "wood slick" from the ship's cargo.
Conditions on Monday prevented salvage crews from assessing the state of the ship or towing it back to shore, as 9ft (2.7m) waves and strong winds battered the vessel.
The stricken ship, which weighs 6,395 tonnes and is 328ft (100m) in length, sank at about 0045 GMT on Tuesday.
The Maritime and Coastguard Agency said recovery was "more problematic" once the vessel had sunk, due to the position in which it had come to rest on the sea bed.
The agency warned potential scavengers to stay away from any timber washed up. A vessel with underwater surveillance equipment will check on timber in the ship's hold on Thursday.
The Marine Accident Investigation Branch (MAIB) confirmed it had launched a preliminary administrative inquiry into the incident.