Woods, 34, and Nordegren, 30, issued a joint statement saying they were sad to be ending their six-year marriage, wishing each other the best and promising to work together for their children's happiness.
"We are sad that our marriage is over and we wish each other the very best for the future," it said.
"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."
In Nordegren's petition for divorce, filed at the beginning of July, she claimed the marriage was "irretrievably broken" and asked for her maiden name to be restored.
Woods and Nordegren attended Monday's execution of the divorce at a court in Panama City, Florida, where they agreed to "share parenting" of their children. Both had attended four-hour parenting classes, the court documents showed.
The documents also reveal that Nordegren moved out of the Orlando-area family home in November and moved into another residence nearby. Several newspapers have reported that she intends to move back to Sweden, although the agreement to share custody of the children with Woods might make such an arrangement difficult.
Woods wed Nordegren, a former model, in October 2004 in Barbados and the couple have a three-year-old daughter, Sam, and a 19-month-old son, Charlie.
"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," their joint statement said.
"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."
The divorce was finalized by a Florida judge during a 10-minute hearing Monday in a conference room at Bay Country, Florida. Both Nordegren and Woods were present.
Nordegren's lawyer, contacted by AFP, would provide no information about the terms of her divorce settlement, valued in media reports at anywhere between 100 million and 500 million dollars.
Woods's spectacular fall from grace began on November 27 last year when he crashed his car into a tree and a fire hydrant near his Orlando home.
The incident touched off a massive sex scandal, leading to his admission of adultery and subsequent decision to put his golf career on hold while he tried to rescue his marriage.
"It may not be possible to repair the damage I've done, but I want to do my best to try," Woods wrote on his website. "I am deeply aware of the disappointment and hurt that my infidelity has caused to so many people, most of all my wife and children."
Long seen as an ambassador for a new generation of golfers, Woods's previous clean-cut image had earned him record sponsorship deals and a place in the select pantheon of globally-known sports stars.
According to Forbes business magazine, he was the first athlete to have broken through the billion dollars earnings mark.
That image was decimated in the weeks after the car crash as a string of women, including a porn star, a cocktail waitress and a Las Vegas club manager were romantically linked to the sporting superstar.
Later Woods apologized publicly to Nordegren for igniting the tabloid frenzy in which more than a dozen women claimed affairs, saying he had been "living a lie" and admitting to "doing some ugly things."
In what was widely seen as a bid to save his marriage, Woods was treated for sex addiction at a clinic in Mississippi before making his highly anticipated comeback at the US Masters in March.
Returning at the Augusta National -- a comfortable setting where he has captured four titles, his first in 1997 being the first major crown won by a black golfer -- Woods finished a respectable fourth.
Since then, however, a string of performances ranging from mediocre to poor have seen many question whether the 14-time major winner is capable of recapturing the form that saw him dominate the game for a decade.
Nine months after the sex scandal first broke, Woods enters this week's opening event of the US PGA Tour season-ending playoffs without a win this year.