Brunel, 63, joins the national set-up from Top 14 side Bordeaux-Begles just five weeks before France face Ireland in their Six Nations opener.
His contract stretches to the 2019 World Cup in Japan, Laporte told a press conference at a Paris hotel, and he will be assisted by "a pool of five or six" Top 14 coaches.
Noves, also 63, suffers the ignominy of becoming the first Les Bleus manager in history to be axed.
He has paid the price for the worst record of any France coach with a meagre seven wins from 21 matches, alongside 13 defeats and a humiliating home draw with 2019 World Cup hosts Japan.
His assistants, Yannick Bru (forwards coach) and Jean-Frederic Dubois (backs), were also relieved of their duties.
Brunel was once ex France boss Laporte's right-hand man as forwards coach from 2000-2007.
He took Perpignan to the French league title in 2009 and spent five years in charge of Italy between 2011 and 2016 before switching to Bordeaux in 2016.
Brunel will officially begin the task of rebuilding the national side next week, Laporte said.