Murray sank to his knees and rolled in the clay of the Flanders Expo after his successful topspin lob sealed a straight-sets defeat of David Goffin and Britain’s 3-1 win over Belgium.
It capped the team's extraordinary rise from the third tier of the competition five years ago and a milestone-laden, landmark campaign from Murray himself.
"It's an amazing feeling. I imagine it will take a few days before it really sinks in," said the world No2, who was hoisted onto the shoulders of jubilant team-mates upon winning.
"I probably haven't been as emotional as that after a match that I've won. I've been pretty upset having lost matches before, but I'd say that's the most emotional I've been after a win.
"It's incredible that we managed to win this competition. I didn't know that would ever be possible. It's great.
"For all the team it's great to have Davis Cup next to our name. We'll all remember this year for the rest of our lives, regardless of what happens. Nothing may ever top this now."
Murray, 28, overcame a raucous and overwhelmingly partisan home-supporting crowd to beat world No16 Goffin 6-3, 7-5, 6-3 in a little under three hours.
He again had a hand in all three of Britain's winning rubbers in the tie, helping brother Jamie win Saturday's doubles and beating Ruben Bemelmans in Friday's singles clash.
In doing so, the Scot achieved a number of milestones. He became only the second man to win the trophy with a 8-0 singles record, after John McEnroe, and only the third man in the modern era to do so at all; the first player since Pete Sampras to win three live rubbers in the final; and only the fourth man to contribute to 11 successful rubbers.
"Yeah that's obviously nice. I was just really, really pumped the whole match, really, really focused," he said.
"To have won all the singles matches I've played this year is great. I'm glad I was able to help the team. There's only been I think two players who had won eight singles, so to do that is nice. It doesn't happen too often. I'm proud of that."
Murray cited the quarter-final victory over France at Queen's Club in July as the point he began to believe Britain's current crop could emulate Fred Perry's class of 1936.
"That was an incredibly hard match to win. They have a great team with a lot of top players," he said. "The match against [Gilles] Simon was incredibly tough mentally and physically. Once we got through that, I really felt like we had a chance to do it."
Murray joined peers Novak Djokovic, Roger Federer and Rafael Nadal in achieving Davis Cup glory and is only the third man to add the title to Wimbledon success and Olympic gold.
He praised captain Leon Smith and team-mates James Ward, Kyle Edmund and Dan Evans for a run to the final that also featured wins over the United States and Australia.
"Since Leon has become captain I think you just look at the results and see where we've come from," he added. "Leon and his team are responsible for getting us to play at that level so consistently and deserve a lot of the credit for that."