Major Pete Rowlands and Captain Mark Waterson, both of Long Riston, near Beverley, together with team mates from Devon and Gloucester were within a mile and a half of Mevagissey in Cornwall, when they were blown back out to sea in "appalling" weather.
They eventually had to agree to a tow, which put paid to their bid to become the first Britons to row the 3,300-nautical miles between the US and UK coastlines.
The attempt to set a mainland-to-mainland record was an additional effort which the team put in after taking part in a race to the Scilly Isles.
They and their 29ft craft had been at sea since leaving New York on June 10, rowing under the name Team Hesco.
Lizzie Bell, spokeswoman for the team, said: "They were within sight of land but were blown back out into the channel in very bad weather and were unable to row against the wind.
"They took the difficult decision to get towed in because of the conditions. The food supply was non-existent and they were exhausted.
"They have been very unlucky all the way across. They are very thin, very shaky, very emotional and having trouble finding their land legs.
"It has been an incredible effort."
They have so far raised more than £142,000 for the Meningitis Trust following the death of Major Rowlands' 16-year-old son Gareth from meningitis three years ago.
The intrepid rowers came in behind two other boats in the Shepherd Ocean Fours Rowing Race, which finished in the Scilly Isles.
The first place went to a boat crewed by an American university team, while another – also crewed by Yorkshire soldiers – arrived last Saturday.
Team Hesco survived numerous hazards, including force nine winds from tropical storm Alberto. The men were driven backwards despite spending 12 hours a day at the oars.