Britain headed into the final day leading 2-1 after Murray and his brother Jamie secured a crucial win in the doubles on Saturday with Leon Smith’s team counting on the world number two to secure a famous win.
Murray delivered in emphatic fashion winning 6-3 7-5 6-3, despite a dogged resistance from a fiercely-determined Goffin, to clinch an 11th personal victory in this year’s competition and Britain’s first Davis Cup title since 1936.
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"I just can’t believe we did it," said Murray. "I never thought I would. It’s amazing. I’ve always played some of my best tennis when I play for my country.
"A massive thank you to everyone who came to watch, all of the fans, the Belgians and the Brits. David's a great player. He is unbelievably talented. He made it a very tough match. I’d imagine we’ll have a party tonight."
[PHOTOS: Great Britain and Andy Murray celebrate Davis Cup triumph]
For Murray, who clinched victory with a breathtaking point having dropped just two sets in eight singles rubbers, it was another memorable career highlight with his team-mates on hand to join the wild celebrations.
[As it happened: Andy Murray bt David Goffin]
The 28-year-old did not wait to put Goffin under immense pressure from the outset and secured a crucial break of serve with a stunning display of power hitting from the back of the court in the sixth game of the match to seize control.
The world number two broke to love with an imperious string of points and went on to take the opening set 6-3 in commanding fashion, despite fierce resistance from Goffin on the indoor clay of Flanders Expo.
[REACTION: 'Andy Murray the greatest thing for British tennis... ever!']
Murray, who has a formidable record from one-set up in matches, saw Goffin force a break point in his first service game of the second set, but the Belgian could not capitalise to seize an early advantage.
The Brit proceeded to power through a series of games winning an astonishing 18 successive points on serve to keep pace with Goffin before eventually breaking with the set finely poised at 5-5.
Murray refused to let his level drop at all as he took the second set with unerring confidence to give himself a cushion with Britain expectant at just one set away from glory.
With Goffin able to play with greater freedom from a losing position, the 24-year-old put Murray under considerable pressure in the third set, repeatedly taking the Brit to deuce on his serve.
But when it really mattered Murray, who had won both previous matches against Goffin in straight sets, was able to repel his obdurate opponent and secure an inspired break in the seventh game with a flurry of brutal groundstrokes.
It was ultimately fitting that Murray, who has been Britain's reliable and consistently brilliant leader throughout the Davis Cup campaign, was the man to close out a famous triumph in tennis's premier team competition.
Murray, who already had Wimbledon and US Open titles to his name, as well as an Olympic gold, has now inspired Britain to yet another memorable and historic crown. For the Scot and his team-mates, this was a most magnificent way to end the year.

Great Britain lift the trophy

Leon Smith makes a speech

Post-match analysis

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