Woods, 38, underwent a successful microdiscectomy in Utah to correct a pinched nerve in his back.
The world number one has been struggling with his fitness for several months - pulling out of Bay Hill recently, and falling away when in contention at Doral - and had already indicated that he was not sure whether or not he would be able to play.
But the 14-times Major champion confirmed on Tuesday that he will miss the event at Augusta for the first time since 1994.
Woods said he would begin intensive rehabilitation and soft-tissue treatment within the next week and expected to start chipping and putting in about three weeks, as long as his recovery went according to plan.
He said he risked further injury had he kept playing because of the repetitive motion from golf but there should be no long-lasting effects from the surgery and he hoped to resume playing by the middle of the year - suggesting that he might be fit in time for the US Open at Pinehurst in June and the Open Championship at Hoylake in July.
"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 on his official website.
"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.
"I'd also like to thank the fans for their support and concern. It's very kind and greatly appreciated. This is frustrating, but it's something my doctors advised me to do for my immediate and long-term health."
Woods has been plagued by back problems since last year - and indeed for much of his career - but his condition worsened last month.
He failed to finish the Honda Classic at Palm Beach Gardens in early March, quitting after 13 holes in his final round.
Then he tweaked his back again on the last day at the WGC-Cadillac Championship at Doral in Miami a week later, tumbling out of contention with a final-round 78 to finish tied for 25th.
He then pulled out of the Arnold Palmer Invitational at Bay Hill - a tournament he has won eight times, including 2012 and 2013 - in the hope that he could play at the Masters before opting to undergo surgery instead.
Woods has missed just a handful of Major championships in his career, the most famous example coming when he missed the 2008 Open Championship and US PGA Championship after knee surgery.
He also missed the 2011 US Open and Open Championship due to more knee problems.
The Masters, which he has won four times, is the only one of golf's Majors which he had yet to miss since turning professional in late 1996.
He played the event twice as an amateur back in 1995 and 1996, earning entry as the previous year's US Amateur champion.
And it was his 1997 victory at Augusta which announced him to the world as a legend in the making, winning by a record 12-shot margin.
Woods won the event three more times, in 2001, 2002 and 2005 - and though he has not won it again, he has since finished outside the top six only once.
The superstar's tally of 14 Majors is four short of the all-time record of 18 held by Jack Nicklaus. He has also won 79 PGA Tour events, three behind Sam Snead's record of 82.
His latest injury is sure to raise fresh doubt about whether he will ever break those records but Woods remains adamant that time is still on his side.
"It's tough right now, but I'm absolutely optimistic about the future," Woods said.
"There are a couple records by two outstanding individuals and players that I hope one day to break.
"As I've said many times, Sam and Jack reached their milestones over an entire career. I plan to have a lot of years left in mine."
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