He is dating 28-year-old US skier and Olympic gold medallist Lindsey Vonn.
Woods, 37, divorced from his 33-year-old Swedish wife Elin Nordegren, a former model, in 2010 after admitting a string of affairs.
He posted four photographs on his Facebook page and wrote: "Something nice that's happened off the course was meeting Lindsey Vonn. Lindsey and I have been friends for some time but over the past few months we have become very close and are now dating.
"We want to continue our relationship, privately, as an ordinary couple and continue to compete as athletes."
Vonn, who with her long blonde hair bears a resemblance to Woods' ex, also announced the relationship online.
She wrote: "I guess it wasn't a well-kept secret but yes I am dating Tiger Woods.
"Our relationship evolved from a friendship into something more over these past few months and it has made me very happy."
She added that she would like to keep "that part of my life" private.
Between them, they have six million followers on Facebook.
Vonn won a gold medal in the 2010 Winter Olympics. Woods reportedly sent his private jet to collect her when she injured her knee earlier this year.
He has a daughter Sam, five, and son Charlie, four, with Ms Nordegren. Lindsey was married to US skier Thomas Vonn for four years but they divorced in January.
