The 92ft Royal and Sun Alliance was due to cross the finishing line off the Lizard, Cornwall, last night.
She was then expected to sail straight back to Hamble, Hants, and is set to arrive this afternoon.
Light and variable winds sank her attempt to beat the French-held "all- comers" speed record. But, as the first all-female crew to take on the 2,925 nautical mile speed challenge, their time will stand as the mark to beat.
The catamaran, which set off from New York on Sunday last week, was chasing Serge Madec's 1990 time of six days, 13 hours and three minutes.
The transatlantic crossing is the first of three voyages by the 10 women - all firsts by an all-female crew.
In August they will attack the Round Britain and Ireland sailing record of five days, 21 hours and five minutes.
And in December they will take part in the Jules Verne Round the World trophy challenge.
During her latest voyage, Ms Edwards described the hardships she and the crew were facing, on the same waters which had claimed the Titanic.
She said on a ship-to-shore call: "The weather is pretty horrendous. It is five degrees below freezing with the wind right on the nose, making the boat toss around or shudder through the waves. Just when you think you have got your balance, it pitches. There are a few bumps and bruises and several of us are feeling pretty queasy.
"Everyone is drenched to the skin and having to sleep fully clothed, so that they can be ready to deal with icebergs. When you see them on radar it's worse than seeing them for real, because as you hurtle through the blackness your imagination works overtime."
However, despite the discomfort, Ms Edwards said her international crew had been "fantastic". She added: " All that matters is the weather, the sea, and what you are doing on board at the time".