The ban was first proposed by the Royal & Ancient and the United States Golf Association in November. Players and the golfing community were then given 90 days in which to discuss the proposal.
The European Tour expressed its support for the idea but both the US PGA Tour and PGA of America voiced opposition.
"We took a great deal of time to consider this issue and received a variety of contributions from individuals and organisations at all levels of the game," R&A chief executive Peter Dawson said in a statement.
"We recognise this has been a divisive issue but after thorough consideration we remain convinced this is the right decision for golf," he added ahead of this week's PGA Championship at Wentworth, England.
USGA president Glen D. Nager said the new rule would uphold the "essential nature of the traditional method of the stroke and eliminate the possible advantage that anchoring provides".
"Having considered all the input that we received, both before and after the proposed rule was announced, our best judgment is it is necessary to preserve one of the important traditions and challenges of the game - that the player freely swing the entire club," said Nager.
While anchoring will be banned from 2016, long putters can still be used as long as players freely swing the club away from their bodies.
Golf could become extremely muddled, or messy at the very least, as it waits to see whether the US Tour and the PGA of America back the ban.
"The PGA Tour acknowledges the USGA has adopted Rule 14-1b which prohibits anchored putting as of January 1, 2016," it said in a statement.
"We will now begin our process to ascertain whether the various provisions of Rule 14-1b will be implemented in our competitions. We will announce our position regarding the application of Rule 14-1b to our competitions upon conclusion of our process."
November's announcement by the rulemakers came after three of the previous five Major champions had used 'belly' putters - Keegan Bradley (2011 US PGA Championship), Webb Simpson (2012 US Open) and Ernie Els (2012 Open Championship).
Australian Adam Scott then followed suit when he won last month's US Masters while using a long putter anchored to his chest.
Dawson said the recent successes in Majors by players using anchored putters had not been a factor.
"No, I can say unequivocally that that had absolutely no impact," he told Sky Sports News.
"The greater concern was the increasingly widespread use of them in Tour events, up to 26 percent in one case. There was also the concern that young people coming into the game are being taught that that is the way to putt."
Many of the game's leading players, including world number one Tiger Woods and second-ranked Rory McIlroy, have backed the ban.
"I just believe the art of putting is swinging the club and controlling nerves," 14-times Major champion Woods said.
"Having it as a fixed point ... is something that's not in the traditions of the game. We swing all other 13 clubs. I think the putter should be the same."
South African great Gary Player welcomed the joint announcement.
"Must congratulate the R&A," he said. "I think three years is a long time - I think one year would have been right but I'm not going to argue with it.
"I spent hours and hours training my mind to have good nerves under pressure. The long putter takes away the nerves, it allows you to hide the nerves and nerves are an integral part of the game of golf."
Eight-times European number one Colin Montgomerie also agreed with the ban.
"Glad to see that common sense has prevailed," said the Scot. "I have used an anchored putter and it was easier to putt with it, rather than without, but I'm in favour of the ban."
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