He is playing the Arnold Palmer Invitational this week at Bay Hill, where he is a seven-time winner and the defending champion. 1 in the world for the first time since October 2010 if he wins.
After that, Woods is not expected to play until the Masters on April 11-14.
His marriage of five years to Elin Nordegren of Sweden collapsed in 2010 after shocking revelations of multiple extramarital affairs.
She is the only skier — male or female — to win one of the annual AP awards that date back to 1931.
Dominant against other top female skiers, Vonn petitioned the International Ski Federation to let her compete against men in a downhill race, but the request was rejected last year.
Her 59 career World Cup race victories is three shy of the record, and she recently claimed a sixth consecutive World Cup downhill title.
"Our relationship evolved from a friendship into something more over these past few months and it has made me very happy." Both said they wanted to keep everything else private.
Woods posted four photos with Vonn on his page, while Vonn's had one of those photos.