Woodgate joined Stoke on a free transfer this summer, after struggling with injuries during his spell at White Hart Lane.
O’Hara told The Sun: “He’s phenomenal. He’s one of the best centre-backs in the league. If he stays fit, what a signing he’ll be.
“I am surprised a few more didn’t go in for him and take a punt.
“He told me over the summer he was fighting fit. I’m very surprised Harry decided to let him go. Spurs have a lot of midfielders but are not exactly bulging at the seams with defenders.
“Woody showed straight away in Europe with Stoke he is still top class. It could turn out to be an error, yeah.”