Marquez has never coached a top-flight side but gained popularity at Las Palmas by guiding their reserve team to promotion from the Tercera Division to the Segunda Division B in his first campaign with the Canary Islands club.
He has previously coached Espanyol's reserve side and will work alongside former Spain international and Las Palmas fan favourite Juan Carlos Valeron.
The club had reportedly hoped to finalise a deal with former Palermo coach De Zerbi but he was unable to join because of a contractual issue with the Italian club.
Las Palmas were promoted to the top flight in 2015 and lit up the league last season with their bold, attacking style under Quique Setien but they went off the rails in the second half of the campaign, winning four games from their last 19.
Setien resigned in March.
(Reporting by Richard Martin, Editing by Ed Osmond)
