Woods, who receives about $100m (£60m) a year from his sponsors, issued a statement on his website yesterday, saying "I have not been true to my values and the behaviour my family deserves."
He continued: "I am not without faults and I am far short of perfect. I am dealing with my behaviour and personal failings behind closed doors with my family."
Speculation has surrounded Woods since he crashed his Cadillac into a fire hydrant and tree outside his Florida home in the early hours of last Friday.
However, following yesterday's apology, many of Tiger's sponsors have come out and said that their sponsorship deals would remain unchanged.
Gatorade, owned by Pepsico, said: "Tiger and his family have our support as they work through this private matter. Our partnership continues."
Procter & Gamble's Gillette said: "At this time, we are not making any changes to our existing marketing programmes. As a matter of policy, we don't comment on future marketing plans."
Nike said: "Nike supports Tiger and his family. Our relationship remains unchanged."
Electronic Arts, TCL Vision and private jet hire company NetJets also said that they would continue to support Woods.
AT&T, Accenture, Tag Heuer and Upper Deck could not be reached in time for publication.