The Skandia Ocean Row team had been bidding to beat the 55-day record for completing the 2,100-mile journey from Newfoundland in Canada.
They had been on schedule to beat that target by more than 10 days - while also striving to better the 35-day record for a crossing of the Atlantic in either direction.
This record is held by the Gerard Seibel team, which sailed from Tenerife to Martinique in La Mondial in 1992.
However, storm damage brought the Skandia Ocean Row effort to a premature end last week at the half-way point.
Their 30ft rowing boat was picked up by a diving support vessel and taken back to the UK.
The four-man team was led by Poole-based firefighter Mark Stubbs, who was accompanied by George Rock and Nigel Morris from Teesside and Rob Munslow from Monmouth.
They arrived in Aberdeen on Monday morning for an emotional reunion with their families.
Mr Morris said: "It is good to be back on dry land, although obviously we wished it had finished a different way."
World record
Mr Rock said the team was "devastated" that one problem with the boat had scuppered the effort.
The crew set off from Newfoundland on 11 June, but their effort came to an end following damage sustained in a storm on 30 June.
While they were initially able to repair the rudder using spare parts, it broke again on 2 July.
The 55-day world record was set by the two-man team of Harbo and Samuelson in 1896, who rowed to the Isles of Scilly in an 18-foot wooden whaler boat called the Richard K Fox.
Their achievement was tied only by solo rower Tom McClean, who matched their time 90 years later in a boat called Skoll 1080.
The Scot, who was the patron of the latest attempt on the record, was among those waiting in Aberdeen as the team arrived on British soil.
The men were planning to spend the night in Scotland before travelling home on Tuesday.
However, they have already stated their intention to try the trip again next year.