France appeared to gain an advantage when they refused Wales' request to close the Millennium Stadium roof against the heavy Cardiff rain, but the home side weathered the conditions and the opposition.
Alex Cuthbert illuminated a frustrating encounter with a moment of class midway through the first half.
Wales worked the ball to Cuthbert from a turnover and the giant wing shimmied inside, outside and inside again to beat three men and go over the line.
England's defence of their title ended with second place after their overhauled side powered to a 30-9 win over Ireland, who finished third. Scotland finished last after losing 13-6 to Italy.
France displayed resolute defence and only belatedly showed any ambition to carry the game to Wales, who emerged a worthy winner through Cuthbert's brilliance and 11 points from the boot of fullback Leigh Halfpenny.
Inconsistency has been Wales' most reliable characteristic in recent seasons, with Grand Slams in 2005 and 2008 followed by fifth- and sixth-place finishes. With coach Warren Gatland contracted until 2015, Wales will hope this latest triumph lays the platform for a period of dominance similar to that enjoyed from 1969-79.
In that period, Wales won the old Five Nations seven times - including three Grand Slams - and shared the title twice more, losing only seven matches in 11 years and not a single one at home.
"We're quite a young team so this is the first chance for a lot of us to win anything," flanker Dan Lydiate said. "We're over the moon."
Lydiate's work at the breakdown and covering defense, Cuthbert's tackle-busting surges on the flanks and in midfield and scrumhalf Mike Phillips' composure were instrumental in Wales' 11th Grand Slam - one short of England's record mark.
Wales props Gethin Jenkins and Adam Jones and substitute back-rower Ryan Jones are the only three Wales players to have played in all three of the most recent Grand Slam-winning teams. And the trio all played important roles on Saturday.
Jenkins and Adam Jones formed the foundation of a superior scrum and Ryan Jones, who captained the 2008 team, helped repel the resurgent French in the second half, having replaced captain Sam Warburton at the interval.
Wales also avenged their semifinal loss to France at the 2011 Rugby World Cup when Warburton was sent off for a dangerous tackle.
"The occasion didn't get to us as much as they would have hoped," center Jamie Roberts said. "The coach has given us freedom to go out and play.
"The World Cup brought us tighter and losing to France spurred us on to get some revenge."
Andy Robinson's future as Scotland coach was in doubt after his team ended a promising campaign in last place with just four tries scored.
Robinson could point to unfortunate yellow cards to Nick de Luca and James Hamilton that forced Scotland to play a quarter of the match with 14 men but Italy scored the only try through Giovambattista Venditti to further improve its Six Nations record to six wins from 13 matches against the Scots.
The game burst into life minutes after the break as a move down the left flank ended with Venditti racing onto Kris Burton's short pass to touch down.
Italy could have won by even more but Mirco Bergamasco missed two place kicks on goal. Greig Laidlaw scored Scotland's only points with two penalties.
Robinson, who is contracted through the 2015 Rugby World Cup, said he would meet Scottish Rugby Union chief executive Mark Dodson in the next few weeks to discuss his future.
"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," Robinson said. "We'll be doing a debrief of the Six Nations.
"There is not a set time scale 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."
