Wayne Pivac’s side narrowly lost out on a Grand Slam last weekend when they were beaten 32-30 by Les Bleus at the Stade de France.
It meant Wales had a nervous wait to see if they would win the title.
France needed to beat Scotland by 21 points or more and score four tries in the process, but in the end they managed neither which meant Wales came out on top.
Pivac and his players – who sealed a Triple Crown earlier in the tournament – will lift the Six Nations trophy at their Vale of Glamorgan training base on Saturday.
Pivac said: “It was a hell of a game wasn’t it? It reminded me of last week with the cards, people coming and going, penalties and missed opportunities. What a tournament it’s been.
“From a Welsh point of view we’re very happy to have won the Championship. It’s a shame we couldn’t have done it as a group last week.
“We don’t want to talk too much about last week, but we felt we did quite a bit in that game to have won it. As a game it wasn’t to be. It doesn’t take away from all the hard work that was done.
“We’ve come out on top of the points table and have won the tournament.”
Scotland sealed a dramatic win over France thanks to an 85th minute try from Duhan van der Merwe.
It came following their fly-half Finn Russell being red carded for leading into Brice Dulin’s neck with his forearm but despite losing their playmaker, Scotland were not to be denied.
Van der Merwe started and finished their scoring while David Cherry also crossed. Russell kicked the rest of the points save for Adam Hastings’ conversion of Van der Merwe’s second.
France scored through Dulin, Damian Penaud and Swan Rebbadj, but they couldn’t stop Scotland from sealing a first win in Paris since 1999.
Their captain Stuart Hogg was yellow carded, but after Russell was dismissed, France’s Baptiste Serin also went to the sin bin and Van der Merwe won it at the death.
Pivac added: “Some great rugby has been played in this tournament – it’s exciting times for all concerned. We’re very happy with how things are going at the moment in our camp.
“We built throughout the competition. We’ve just watched Scotland and they did an amazing job and took some big scalps. It’s been a great period for Gregor [Townsend] since the World Cup – I’d like to congratulate him on that performance which has helped us win the Championship.”