Both attended Bay County Circuit Court in Panama City, Florida so that the divorce agreement could be executed.
Details of the financial settlement Miss Nordegren will receive were not revealed but estimates have ranged from $100 million (£65 million) to $750 million (£480 million).
Experts have said the settlement could be one of the largest in celebrity history, dwarfing the $150m (£100 million) paid by Michael Jordan, the basketball star, to his former wife Juanita.
In a statement Woods and Miss Nordegren said:"We are sad that our marriage is over and we wish each other the very best for the future.
"While we are no longer married, we are the parents of two wonderful children and their happiness has been, and will always be, of paramount importance to both of us.
"Once we came to the decision that our marriage was at an end, the primary focus of our amicable discussions has been to ensure their future wellbeing."
The couple have two children, Sam Alexis, 3, and one-year-old Charlie Axel.
In their statement they went on: "The weeks and months ahead will not be easy for them as we adjust to a new family situation, which is why our privacy must be a principal concern."
A source close to Miss Nordegren, 30, said: "She's feeling OK about all this. She's been through hell but handled herself with such dignity. And now she's got a whole new life ahead of her."
According to the divorce documents the marriage was “irretrievably broken” and the couple had agreed to separate in early July.
Woods and Miss Nordegren will share parenting of their children, and Miss Nordegren will re-assume her maiden name of Elin Maria Pernilla Nordegren.
Both have gone through a four-hour parenting course as they prepare to look after their children separately, celebrity website TMZ reported.
In November Woods, 34, crashed his car into a tree in the early hours of the morning outside his home in Florida.
The crash was said to have followed an argument with his wife and a string of women began coming forward alleging affairs.
He then lost several major sponsors after the sordid allegations became public. He is thought to have lost up to $35 million (£23 million) in sponsorship money following last year’s sex scandal.
In a televised statement in February he admitted being unfaithful and said he had been "selfish and stupid".
Woods then took an indefinite break from golf and committed to working at his marriage.
But Miss Nordegren was said to be furious over a television advertisement he filmed for Nike which featured the voice of his late father.
It was broadcast on the eve of the tournament and featured Woods looking directly into the camera without speaking.
A 2004 recording of his late father Earl saying "Did you learn anything?", was played over the footage.
At the time a source said: "Elin was violently angry over this commercial and thought it was a cheesy thing to do."
She was also said to have thought her husband would take more time off before returning to the course.
Miss Nordegren, 30, a former swimwear model from Sweden, bought a property there last year.
It has been undergoing renovation leading to further speculation that she may move home.
She had accompanied Woods to counselling and rehabilitation sessions in recent months but had been seen not wearing her wedding ring in public.
An original prenuptial agreement is believed to have given her the right to $20 million (£12 million) after 10 years of marriage.
But in the wake of the scandal that was said to have been renegotiated, which could have led to her receiving hundreds of millions of dollars.
Woods is understood to be keen that she never reveal details of their marriage publicly.