Woods, 34, and Elin Nordegren, 30, issued an amicable 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.
Both Woods and Nordegren attended Monday's execution of the divorce at a court in Panama City, Florida, where they agreed to joint custody of their three-year-old girl Sam and one-year-old boy 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," the 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."
Nordegren's lawyer, contacted by AFP, could provide no information about the terms of the 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 near his Orlando home in bizarre circumstances.
The incident touched off revelations about 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.
The string of affairs left Woods's picture-perfect image as the faithful husband in tatters and the billionaire golfer began to lose valuable marketing contracts.
"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."
Later he apologized publicly to Nordegren for igniting the tabloid frenzy in which more than a dozen women claimed affairs.
Woods, who said he had been "living a lie" and admitted to "doing some ugly things," received therapy at a sex addiction clinic before making a highly anticipated comeback at the US Masters in March.
Returning at the August 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.
Woods enters this week's opening event of the US PGA Tour season-ending playoffs without a win this year.
Stripped of his invincible aura, Woods ranks only 108th in the points race and could at any moment lose his number one ranking.
Without a good finish at The Barclays, starting on Thursday, it could be his final outing of the season, as only the top 100 qualify for the next event.
Despite his woes, US Ryder Cup captain Corey Pavin says Woods is high on his list of captain's picks for the biennial match against the best European golfers -- to be contested this October at the Celtic Manor in Wales.