The LaLiga outfit revealed in a statement on Monday that the 48-year-old has been handed the reins on a 12-month deal with an option for a second year.
Takes over after record-breaking year with Las Palmas Atlético
Márquez led the club's second team, Las Palmas Atlético, to promotion to Segunda División B last term, in a campaign that saw his side achieve the highest ever points total in Tercera División Group VII.
"Márquez knows this club down to the ground," said Las Palmas president Miguel Ángel Ramírez. "We're all very happy - we feel he is the best option."
"Coaching Las Palmas is a dream come true," Márquez told the club's website.
Márquez to be presented as new boss on Tuesday
The former AE Prat, CE Europa, CF Badalona and Espanyol B coach is to be officially unveiled by Las Palmas at the Estadio Gran Canaria on Tuesday.