It is the 29-year-old Cuesta's first role as a head coach after spending the past five years as an assistant at English Premier League club Arsenal.
Parma announced on Thursday that Cuesta had signed a two-year contract with the option of a third year.
Cuesta has experience in Italy, having been an assistant coach with the under-17 team at Juventus for two years. He also worked with Atletico Madrid's youth teams prior to that.
Cuesta, a Mallorca native, is the second-youngest coach ever to work in the Italian top flight.
In 1939, Elio Loschi was 29 years 9 months 20 days old when he took charge of his first match as player-coach at Triestina.
Cuesta will be 30 years 26 days old when he takes to the dugout for Parma's first match, coincidentally also against Juventus.
Italian media reported that Cuesta took his first steps into coaching when he was studying in Madrid. He messaged members of the technical staff of both the city's teams on social media until the then-coach of Atletico's under-12 team responded.
Parma's previous coach Cristian Chivu left the club last week, after steering the team to Serie A safety, taking over instead at Inter Milan.
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