The Englishman, who finished second in both the Masters and the Open this year, ended Woods' 281-week reign at the top after Martin Kaymer failed to pip him to the post after Sunday's finish to the Valderrama Masters.
And Woods acknowledged Westwood, who at one point in his career slipped out of the top 200 in the rankings, is a worthy number one.
The American told BBC Radio 5 Live: "Look how well he's finished in the major championships. He hasn't won one but he's come so close. It's just a matter of time.
"Lee's been by far the most consistent of all the players in the majors over the last two years. You don't necessarily have to win. It helps, but if you're finishing in the top three or four at a major championship you're racking up so many points and he's done that over the last couple of years better than anybody.
"He's made enormous leaps with his game, he was struggling for a few years and turned his whole game around."
Woods will have his first chance to return to his habitual status when he competes in this week's HSBC Championship in Shanghai, and he is confident he can bounce back from the loss of top spot.
"I've been there before," he said. "I've been there many times actually, it's one of those things.
"I won the Masters in 1997, changed my swing - then went from the middle of '97 to the middle of '99 with only one win. After that I had some pretty good years.
"I go into every tournament to try to win. There's no sense teeing up if you're not there to win.
"Every year it's getting more difficult because the fields are getting deeper. I don't know how many tournaments I've played in this year where from the cut - the top 70 and ties - to the guy leading the tournament was just eight shots.
"That's unheard of - it's always about 12, 14 shots. But now there are more players that are more consistent and the scores are lower, the cuts are lower."
After the traumatic events of the last 12 months - in which a sex scandal saw him take a break from the game - Woods is ready to focus his efforts once more on golf.
"I'm in a much, much better place," he added.
"I'm much happier, much more balanced. I've gone through a lot and thank God I did, because I needed to put my life back into an order."
With that done, he can once more target the legendary Jack Nicklaus' record of 18 major titles
"It's about finding a balance, and I've done that and I'm moving forward," said Woods, himself a 14-time major winner.
"It's a career. It took Jack over 20 years and I haven't been playing that long. It's a matter of being consistent and I'm working towards that.
"No-one has done better than Jack with 18... at the end of the day, hopefully I'll have more than 18 major championships.
"It's the highest benchmark there is in our sport. I'm close, I have a lot of great years ahead of me."