It was the third time in eight years that Wales had swept all before them in European rugby union’s premier international tournament and was a measure of revenge for their World Cup semi-final defeat by France last year in Auckland.
Wales wing Alex Cuthbert scored the only try of an absorbing match in front of a capacity Millennium Stadium crowd, as the hosts added to their 2005 and 2008 Grand Slams.
“This makes all the sacrifices worth while,” said Wales skipper Sam Warburton, who was sent-off in last year’s World Cup semi-final.
“You have to give credit to the French. They made it difficult for us to get our game going. But we won and that’s what counts.”
Victory also meant Wales had equalled the record of their celebrated 1970s predecessors by winning three Slams in the one decade.
Saturday’s match took place the day after Welsh great Mervyn Davies, captain of the 1976 Slam team, died from cancer.
“It’s a very young team and this was their first chance to win anything,” Wales back-row forward and man-of-the-match Dan Lydiate told the BBC.
“To do it at home in the last match in the Six Nations, what could be better? The crowd were our 16th man, thank you all for turning up.
“Mervyn Davies was a legend of the game and our thoughts go out to his family at this time.”
Earlier, Scotland finished with the wooden spoon as Italy beat them 13-6 in Rome.
The defeat means Scotland have lost all of their five matches in this Six Nations, with their losing streak now extended to seven Tests in a row — a run dating back to last year’s World Cup in New Zealand and their worst since 1998.
For Italy, who scored the only try through wing Giovanbattista Venditti early in the second half, victory saw them avoid the wooden spoon for the first time in five years and gave their French coach Jacques Brunel his first win in charge.
“That (the win) feels good. We’ve had enough good matches in this tournament, we only just lost against England here at the (Stadio) Olimpico for example,” Italy captain Sergio Parisse told Sky Sports.
Scotland have now lost 12 of their 15 Six Nations matches under coach Andy Robinson and this latest defeat is bound to intensify speculation surrounding his position, even though his contract runs until the 2015 World Cup.
“I’m still contracted until 2015. I’m going away to reflect on the Six Nations and reflect on the future, in terms of the positivity that we have, the players we have and the way forward — and putting a plan together for the way forward,” he said.
“There is not a set timescale on that. There’s a lot to take in in terms of what’s happened and it’s about looking at the future and what’s best for the future.
“Now’s not the time to be discussing that, with the feelings that everybody has,” he added.
England and Ireland wrap up this year’s tournament at Twickenham in a 1700 GMT kick-off in what could be interim coach Stuart Lancaster’s last match in charge of the hosts.
The Rugby Football Union is still to announce a permanent successor to Martin Johnson.