The Eide Barge 33 missed the Valhall field by at least 1km (0.6 miles).
More than 300 oil workers were airlifted from the Norwegian sector of the North Sea after the high winds broke the barge's anchor.
Stormy weather in the area has seen waves topping 15m (50ft).
A man died when a huge wave hit another rig earlier in the Troll field off Norway.
The strong winds tore the barge from its moorings and sent it towards BP's Valhall platform, located in the middle of the North Sea between Norway and the UK.
The oil and gas company was forced to shut down output and evacuate staff on board. ConocoPhillips also stopped production and evacuated crew from installations in the same area.
A spokeswoman for the Rescue Coordination Centre for southern Norway told the Reuters news agency that the danger posed by the barge was now over.
"There are no other installations between the barge and the coast of Norway," Borghild Eldoen said.
"It is now up to the owners of the barge to stop it before it reaches the coast."
At one point fears about a collision increased when the barge - 110m in length and 30m wide - changed course and headed straight for Valhall, BP  Norway spokesman Jan Erik Geirmo told the AFP news agency.
But in the event it floated away from the evacuated platforms.
Mr Geirmo said that a tug had been deployed to immobilise it - an operation which will be dangerous in such stormy conditions. He said the situation was now returning to normal and employees will progressively return to the platforms.
Norwegian media said the barge ran adrift on Wednesday evening some 25km (15 miles) from Valhall.

The channel's signed a deal with 20th Century Fox to show new episodes of Family Guy from later this year.
The agreement also includes other Seth MacFarlane animated comedies American Dad, The Cleveland Show and new series Bordertown.
Family Guy has been a major part of the BBC Three schedule since 2006, becoming one of the channel's highest rating shows.
But it's not the last we'll see of the Griffins on the BBC as the corporation has one more new series to show - the one currently being broadcast in the States.
The BBC also still has rights to repeat episodes from previous series - for the moment.
The BBC says Family Guy will be on the BBC for "at least the next two years".
There's been discussion over what would happen to the offbeat comedy, given plans to move BBC Three online.
More than 270,000 people have signed a petition against the move.
The BBC said: "We are incredibly proud that the BBC has successfully aired Family Guy for the past nine years and built the series into such a hit in the UK.
"However, when a show becomes so successful it often becomes a target for other broadcasters.
"We are sorry that it will not have a long term home on the BBC."
Follow @BBCNewsbeat on Twitter, BBCNewsbeat on Instagram and Radio1Newsbeat on YouTube

Ann Maguire, 61, was stabbed to death by a 15-year-old pupil at Corpus Christi Catholic College in Leeds in April.
Her attacker Will Cornick, now 16, was jailed for a minimum of 20 years at Leeds Crown Court in November.
The plaque is displayed at the pavilion at Wigan's Mesnes Park where Mrs Maguire sold ice creams as a teenager.
A rose was also planted in the park's memorial garden.
The plaque was unveiled on Friday by Mrs Maguire's sisters, Shelagh Connor and Denise Courtney.
Ms Courtney told BBC Radio Manchester it was "very, very important" to have a memorial in Wigan.
She said: "This was her hometown; she was here for 19 years of her life and she still has family and friends [here].
"She said she wanted somewhere this side of the Pennines for people to go to to remember her without having to travel to Leeds."
Ms Courtney added: "She was an extraordinary person; she touched so many people in so many different ways particularly the students she taught for 40 years."
She said the words on the plaque "capture the essence of Ann and the person she was".
They say: "Ann was one of life's beautiful, sunny and extraordinary people. May her goodness, kindness and generosity of spirit continue to be an inspiration to us all and may her memory never be forgotten."
A memorial service was held in Mrs McGuire's memory on Thursday, featuring a choir consisting of many of her former pupils.
A potential major disaster in the North Sea has been narrowly averted after a large, unmanned barge went adrift in stormy high seas and came close to colliding with offshore oil platforms.
[NEXT_CONCEPT]
The Griffin family is moving home - to ITV2.
[NEXT_CONCEPT]
A plaque dedicated to a murdered school teacher has been unveiled in her hometown in Greater Manchester.