The Flying Phantom sank in freezing fog in December 2007 while towing a cargo vessel on the River Clyde near Glasgow.
At the High Court in Glasgow today, tug company Svitzer Marine Limited pleaded guilty to a series of health and safety breaches including failing to put in place a safe operating procedure following the grounding of the Flying Phantom in foggy conditions in a previous incident in December 2000.
Stephen Humphreys, 33, from Greenock, Inverclyde, Eric Blackley, 57, from Gourock, and Bob Cameron, 65, from Houston, Renfrewshire, died when the tug sank.
A fourth man, Brian Aitchison, 37, from Coldingham in the Borders, was rescued.
The accident happened when The Flying Phantom was towing the Red Jasmine vessel in the Clyde Harbour area on the evening of December 19.
Dense fog severely restricted visibility and the crew could not see the boat they were towing.
The larger vessel overtook the tug and caused it to capsize.
Svitzer Marine admitted "failing to ensure, as far as reasonably practicable, the health, safety and welfare at work" of the crew.
The Flying Phantom suffered £150,000 of damage when a vessel it was towing on the Clyde in 2000 collided with the tug in similar circumstances, the court heard.
Svitzer Marine Limited said it "greatly regretted" the health and safety failures which led to the tragedy.
Peter Gray QC, acting for Svitzer, said the company was a "conscientious and reputable" employer that took pride in its safety record before the incident.
"Ever since December 19 2007, it has been a matter of the greatest regret that, in relation to the towing in restricted visibility, it failed to meet the very high standards it sets itself," he said.
Stephen Humphreys, 33, from Greenock, Inverclyde, Eric Blackley, 57, from Gourock, and Bob Cameron, 65, from Houston, Renfrewshire, died when the Flying Phantom was overtaken by the vessel it was towing, the Red Jasmine, and capsized.
Lord Turnbull will sentence Svitzer, whose UK office is in Middlesbrough, next month.
Port operator Clydeport Operations Limited is also being prosecuted over the incident. A hearing will take place in Edinburgh in December.