Fournier takes over at the Stade de Gerland after Garde announced that he would not be renewing his contract in order to take a break from football.
The 46-year-old leaves Reims following a four-year spell in which he guided them back to the French top flight, ending a 33-year absence in 2012.
Reims finished 14th in their first season back in Ligue 1 and improved on that showing this term as they ended the campaign in 11th.
Fournier will now look to build on the success he enjoyed at the Stade Auguste Delaune with a Lyon side that came fifth in Ligue 1 in 2013-14, missing out on UEFA Champions League football.
Lyon are to unveil Fournier as their new boss later on Friday.
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