France beat Belgium 3-2 at the Stade Pierre Mauroy in Lille on 26 November to claim the 2017 men's team competition after a 16 year drought.
"@NoahYannick has confirmed his wish to defend the Silver Salad Bowl and will be captain of #TeamFranceTennis @Davis Cup in 2018," the French Tennis Federation announced on Twitter.
The first match of the campaign will be against the Netherlands in Albertville on 2 February.
"You don't change a winning team," said French number one Jo-Wilfried Tsonga, who picked up one point over the three day final.
"It will be good if he stays," added Lucas Pouille, who claimed the decisive point in the singles against Steve Darcis on Sunday.
Noah, 57, who was at the helm for the French triumphs in 1991 and 1996, became only the fourth man to captain a team to three titles in the 117 year history of the competition. Only the Australian Neale Fraser and Niki Pilic, who was born in former Yugoslavia, have been more successful as captains.
"Obviously if I'm going back, it is to win a fourth time for me and an 11th titme for France," said Noah. "We have a real team even though we are playing an individual sport. There is a real connection within the group. It is like a family and this is our strength."
As a result of the victory, France rose to number one in the Davis Cup nations rankings. The last time it occupied top spot was between April and July in 2004.
France also climbed to joint third with Great Britain on the Davis Cup all-time winners list. The United States leads the way with 32 crowns and Australia are second with 28.
France's path to the 2017 trophy was paved with lavish amounts of good fortune. In the first round, they took on a Japan side without their star player Kei Nishikori. The quarter-final opponents, Great Britain, did not have their world number one Andy Murray and Serbia in the semi-finals were without their 12 time Grand Slam champion Novak Djokovic.
Belgium's David Goffin - at world number seven - was the highest ranked singles player that the French team faced. And Tsonga - ranked 15th and Pouille at 18th in the world - failed to conquer him in the two singles matches over the weekend.
Guy Forget, who was captain of the French team which won the Davis Cup in 2001, said: "When you look at the draw that France had this year, we really had to win it. If we'd lost, it would have been very frustrating and there would have been a lot of anger.
"What Yannick did was get the players to focus on the goal of beating a less experienced player on the court. Because the density of French players in the top part of the game is so big, a lot of players brought a point to the team during the campaign."
Noah used eight men and the four who did not feature in the final - Nicolas Mahut, Jeremy Chardy, Gilles Simon and Julien Benneteau - were courtside during all five matches of the final supporting Richard Gasquet and Pierre-Hugues Herbert who been selected along with Tsonga and Pouille. They all lifted the trophy with Noah.
Mahut, 35, who had been expected to play the doubles with Herbert with whom he has won two Grand Slam titles, said: "When I was told I would not be playing I went back to my room and was crying a lot. I had been dreaming my whole life of playing this match.
"But I told myself I had to be strong in front of the group. I'm happy that I did that. There wasn't any part of me that didn't want them to do well. A team can't work like that. I think most of the players who think like that - the team loses most of the time. And I really wnated my team to win."