By Matt Slater
BBC Sport at St Andrews
The 29-year-old American was simply too good this week, and his five-shot victory margin is a fair reflection of that.
A second Open win, both at St Andrews, means Woods now has 10 majors, and he is only the second man to have won each of golf's four big prizes twice.
For Montgomerie there are only the memories of a remarkable week and a fourth runner-up finish at a major.
The 42-year-old Scot was given unstinting support by a passionate home crowd but it was not enough to deny Woods.
Montgomerie, however, gave the galleries and Woods a run for their money.
Playing in the penultimate group with Retief Goosen, the fans' favourite made a superb start to his final round.
Having birdied the third, Montgomerie narrowly missed an eagle putt at the fifth. The tap-in birdie took him to 11 under, one back of Woods in the group behind.
The world number one hit back with a birdie of his own at the fifth and for the next hour they stayed just two shots apart, as Woods missed short birdie putts at seven and eight.
Jose Maria Olazabal, Woods' partner, was also playing well, and when all three birdied the ninth it was clear that this was now a three-horse race.
But Montgomerie's challenge started to fade when he went through the back of the short 11th and failed to save his par.
Sensationally, Woods then drove into a fairway bunker at the 10th - a green he drove on Friday - and also dropped a shot.
The Woods wobble was temporary, however, and when Montgomerie bogeyed the 13th the American seized the moment with a birdie at 12.
After two hours and forty minutes of gripping action, Woods' seemingly precarious two-shot lead was now a commanding four-shot lead over Montgomerie, five over the struggling Olazabal.
The remaining holes saw the classy Californian take complete control of the tournament, and with his putter now co-operating the Claret Jug was in the bag.
Montgomerie kept trying but another shot went at 15 and the last three holes were played in par figures for a nine-under total and another second-place ribbon.
Olazabal also suffered down the stretch but a gutsy birdie at the last lifted him to eight under and a share of third with the 46-year-old Fred Couples - a great return for the veteran American.
One behind this pair, in a six-way tie for fifth, were Geoff Ogilvy, Bernhard Langer, Vijay Singh, Michael Campbell, Sergio Garcia and Retief Goosen.
A shot further back on six under were Kenny Perry and three British players - Graeme McDowell, Ian Poulter and Nick Faldo, who finished birdie, eagle.
Lloyd Saltman, a 19-year-old from Edinburgh, carded a superb 71 for a five under total, one better than his 25-year-old rival from Dundee, Eric Ramsay.
But the main spoils on offer - the Claret Jug and a cheque for £720,000 - belonged to only one man.
Having gone 10 majors without a win after claiming his eighth at the 2002 US Open, Woods has now won the Masters and the Open this year, as well as finishing second at the US Open.
And it is fitting that in the week the golf world said farewell to Jack Nicklaus it should salute the man that will surely one day surpass the Golden Bear's record 18 major titles.
Tiger Woods has won the British Open Championship at St Andrews for the second time. Woods had held the lead at the Old Course since the first day of the championship, with opening rounds of 66-67. He then battled tough conditions on the third day for a 71, and hit a closing round of 70; five shots clear of Colin Montgomerie.

The win at St Andrews marks Tiger Woods' 10th major title of his career.