Noah, who won the French Open in 1983, is taking over from Arnaud Clement and is returning for a third spell in charge.
In his first two stints as captain (1991-92 and 1995-98), Noah led Les Bleus to two titles in 1991 and 1996.
Since then, France have won the Cup once more in 2001 but were beaten in the 1999, 2002, 2010 and 2014 finals.
Clement was named in 2013 and took France to the final last year when they lost to a Switzerland side which included Roger Federer and Stanislas Wawrinka.
France, champions nine times in all, were beaten by Britain in the World Group quarter-finals this year.
With Noah expected to hold a news conference at Roland Garros on Tuesday, Clement was quoted in sports daily L'Equipe saying he was disappointed with how his departure was handled.
"I'm angry at the federation," Clement, who was sacked last week, said on Monday.
"A few days after the defeat (against Britain) in London, the federation contacted Noah to offer him the job," the former Australian Open runner-up claimed.
Noah, one of France's most popular figures, ended his playing career in 1991 and had immediate success with the Davis Cup team when they beat Pete Sampras's U.S. side in the final in Lyon.
Five years later he was at the helm again when France beat Sweden with Arnaud Boetsch saving three match points in the decisive rubber against Nicklas Kulti.
In 1997, he also led the Fed Cup team to their first title.
(Reporting by Julien Pretot; Editing by Martyn Herman)
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