At 19, he was the youngest MotoGP racer of the season. In 2019, he signed to the Petronas Yamaha SRT team, with engineer Diego Gubellini, joining Italian racer Franco Morbidelli. MotoGP World Championship (2019 - ) 2019 He took his firsts pole and win at the Circuit de Barcelona-Catalunya it was the first win for Speed Up since Sam Lowes victory in Austin in 2015. In 2018, he moved to Speed Up, joining Danny Kent. In 2017, he moved to Paginas Amarillas HP40 in the Moto2 class. In 2016, he moved Leopard Racing team with two teammates : Joan Mir and Andrea Locatelli. Near the end of the season, in Misano, he sustained an ankle injury that stopped his progression. In Assen, he scored another podium, finishing third. His second pole position came at the following race in Le Mans. His first Moto3 pole position happened at the Circuito de Jerez. He took his first podium on his second race, at Austin with a second place. On his first ever Moto3 race, in Qatar, he finished 7th. In 2015, Quartararo, then just 15, joined the Estrella Galicia 0,0 Honda team, alongside Jorge Navarro. The rule against participating in the Moto3 World Championship until the age of 16 was repealed in 2014 for the winner of FIM CEV Repsol Moto3 Championship. The next year, being too young to move to Moto3, the age limit being 16, he competed in, and won FIM CEV Repsol Moto3 championship again.

The record had been held by Aleix Espargaró‏‎. He had won the last three races of the season. In 2013, during his rookie year in the FIM CEV Repsol Moto3, at just 14, Quartararo became the youngest ever champion of Spain. He first competed on a 50cc machine at 7 in Spain. Quartararo started racing motorcycle at 4. 1.5 MotoGP World Championship (2019 - ).

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