The British number one beat Belgium's David Goffin in straight sets to give them an unassailable 3-1 lead in Ghent.
It was a fitting climax for the 28-year-old Scot to provide the winning point, having won all 11 rubbers he played in during the campaign as the British defeated heavyweights United States, France and Australia before the clincher against Belgium.
The win over Goffin made him just the third player, after John McEnroe and Mats Wilander, to win all eight singles in the same calendar year since the Davis Cup World Group started in 1981.
Murray, 28, won 11 of 12 points during Britain's first successful campaign since 1936.
