Garde, previously an assistant coach at Lyon and director of their training centre, played for the club for six years between 1987 and 1993, had a spell as a defensive midfielder with Arsenal and also represented France.
However, the 45-year-old has no experience as a head coach.
Lyon said in a statement that a news conference would be held later on Wednesday and president Jean-Michel Aulas would be present for the nomination of Garde "as first team coach".
Former Lille and Monaco boss Puel left on Monday after their disappointing third-place finish in Ligue 1 last season.
Last month French media had linked Lyon with a move for Jean Fernandez but the former Auxerre boss instead joined AS Nancy.
Lyon won the French title seven times in a row from 2002 to 2008 but since Puel's arrival in the second half of that year they flattered to deceive, despite having one of the best lineups in France and better resources than most.
They reached the Champions League semi-finals for the first time in 2010 but that was the high point for Puel, 49, whose side could not keep pace with Ligue 1 champions Lille last term as big signing Yoann Gourcuff failed to shine.
Lyon, who face a Champions League qualifying round tie next term, are due to move to a new stadium dubbed "OL-Land" in the next few years but their status as the undisputed kings of French football is now long gone.
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