Telfer, whose side beat France 36-22 in Paris on Saturday to set up yesterday's finale, watched all the action on TV and could barely disguise his delight. "It is tremendous, unbelievable," he said.
Of Scott Gibbs's last-gasp try which gave Neil Jenkins the chance to give Wales a famous victory and hand Scotland the title, Telfer added: "That was the first time they breached the England defence in the entire 80 minutes."
It is a fitting end to a campaign which saw Scotland score 16 tries, culminating in Saturday's record win.
The favourites to receive the wooden spoon at the start of the tournament, Telfer's men exceeded all expectations.
In John Leslie and Gregor Townsend they had two of the stars of the competition and few will deny them this accolade, Telfer's third championship as Scottish coach, following the previous Grand Slam triumphs in 1984 and 1990.
"It is raining up here," he said from his Galashiels home, "but the sun is shining in my house. England seemed to be coasting I didn't think Wales could do it. But they had a chance to kick which would have taken them nine points clear and I suppose they have paid for that mistake.
"If they had taken their chances there wouldn't have been such a nervous ending. I don't think anyone can deny our brand of rugby has been entertaining," he added. "We have tried to be enterprising and given the crowds something to get excited about.
"England conceded six tries in the competition and we scored three of those. We have deserved our success. We were supposed to be wooden spoonists and I think there is only myself and the rest of the squad who felt we were going to do as well as we did," he added.
The No 8 Stuart Reid, who was winning only his second cap in Saturday's game, spent the afternoon in an Edinburgh bar with fellow Scotland heroes Scott Murray, Martin Leslie and John Leslie.
Unlike Telfer their celebrations were rather more traditional. "It is fantastic, brilliant," said Reid. "We're going to have a few beers and a bottle of champagne.
"Obviously, I only came in for the one game, but I've been around the team all the time and they have been absolutely superb.
"But no one deserves this more than Jim Telfer."
Reid then added his name to that of Kenny Logan and captain Gary Armstrong in pleading with the man who formed part of the coaching team on the 1997 British Lions tour to stay in the job.
"He's honest and hard-working. There is no greater compliment than to see Scotland winning the title again under his guidance.
"But results like yesterday only come along once in a lifetime. These are moments I will cherish forever."