“We are sad that our marriage is over and we wish each other the very best for the future,” the couple said.
They said they planned to “share parenting” of their two children.
News of the split comes nine months after a car crash outside Mr Woods’ Florida home set off revelations that he had been unfaithful to Ms Nordegren.
Details of the financial settlement have not been disclosed, but US media reports suggest the former Mrs Woods will receive over $100m (£64.4m).
The divorce was finalised in Florida by Bay County Circuit Judge Judy Pittman Biebel in what was described as a brief hearing in which both Mr Woods and Ms Nordegren were present.
Correspondents say the agreement is almost certain to have included a secrecy clause surrounding the circumstances leading to the crash which left Tiger Woods seriously injured and after which he publicly confessed to serial infidelity.
BBC golf correspondent Iain Carter says that golf insiders had “guessed… that divorce proceedings have been underway for quite some time”.
“Woods has been a rather more distracted figure than the one we have been used to seeing on the golf course, and of course his results have reflected that,” Carter said.
The couple married in October 2004 in Barbados and have a 3-year-old daughter, Sam, and a 19-month-old son, Charlie.
‘No longer married’
In November 2009 Mr Woods, the world’s wealthiest athlete, was involved in a single-vehicle accident outside his Florida home.
Soon after, several women came forward and claimed they had had affairs with Mr Woods.
Mr Woods, 34 subsequently lost several major sponsors, including AT&T and Gatorade. In February he publicly apologised and admitted that he had been unfaithful to Ms Nordegren, a former model.
In a statement released by their lawyers on Monday, the pair asked for privacy “as we adjust to a new family situation”.
“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,” the joint statement said.
“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 well-being. The weeks and months ahead will not be easy for them.”
Woods, bidding to make the US Ryder Cup team as a “captain’s pick” is poised to play this week at the Barclays golf tournament in New Jersey.