"Sad to say I'm missing the Masters. Thanks to the fans for so many kind wishes," Woods, a 14-time major champion chasing the all-time record 18 majors won by Jack Nicklaus, said on Twitter and on his website.
It will be the first time Woods has missed golf's premier tournament, which starts on Thursday for the 78th time, since he made his debut at Augusta National in Georgia as an amateur in 1995.
It will also raise more question marks over whether he can ever catch up with Nicklaus, although he insists he can still do it.
The surgery was performed on Monday in Park City, Utah, by neurosurgeon Charles Rich, and the 38-year-old will require several weeks rehabilitation.
"After attempting to get ready for the Masters, and failing to make the necessary progress, I decided, in consultation with my doctors, to have this procedure done," Woods said in a statement.
"I'd like to express my disappointment to the Augusta National membership, staff, volunteers and patrons that I will not be at the Masters.
"It's a week that's very special to me. It also looks like I'll be forced to miss several upcoming tournaments to focus on my rehabilitation and getting healthy.
"It's tough right now, but I'm absolutely optimistic about the future," said Woods, who has had a succession of crippling injuries over the last few years to his knees, wrists and now back, the payback for years of employing one of the most dynamic swings in all of golf.
Billy Payne, Chairman of the Augusta National Golf Club, said that he would be missed.
"Tiger was gracious in keeping us updated of his condition and making us aware of his decision.
"We wholeheartedly offered our best wishes for his immediate and long-term recovery. Tiger will be in our thoughts and will be missed by our patrons and all of us at the Masters Tournament next week.
"He is one of our most decorated champions and we look forward to his healthy return in 2015 and beyond."
He may yet be joined on the absent list at Augusta by great rival and three-time previous winner Phil Mickelson, who was forced to pull out of last week's Texas Open with a strained muscle in his side. Earlier in the year he too was sidelined with back pain.
Woods has played in every Masters since 1995 and has become the tournament's star turn and biggest draw. The following year, he missed his only cut at Augusta National just a few months prior to turning pro.
In 1997, in his first major championship as a pro, Woods won the Masters by a record 12 shots, the first of his 14 major titles. He went on to win the Masters in 2001, 2002 and 2005.
Since his last victory at Augusta, Woods has seven top-10 finishes in eight appearances and six top-5s, including last year, when he tied for fourth, four strokes behind winner Adam Scott.
But Woods has endured a nightmare start to a crucial year in his quest to set golf's major win record.
Last month he withdrew in the final round of the Honda Classic, then battled back spasms to a last-round 78 at Doral and skipped the Arnold Palmer Invitational, typically his last warmup for the first major of the year at Augusta National.
He will begin intensive rehabilitation within a week, with doctors estimating he could be chipping and putting again in three weeks, and playing again sometime this summer in time for the US and British Opens.
"It's tough right now, but I'm absolutely optimistic about the future," Woods said.
"There are a couple [of] records by two outstanding individuals and players that I hope one day to break. As I've said many times, Sam (Snead) and Jack (Nicklaus)reached their milestones over an entire career. I plan to have a lot of years left in mine."
Snead won a record 82 PGA Tour events, including seven majors.