Born and raised in Buenos Aires, Varrone began competitive karting and made his car racing debut in Formula Renault 2.0 Argentina at the end of 2016, returning for the full 2017 season and finishing 20th in the standings. In 2018 he moved to Europe and joined the V de V Challenge Monoplace, winning six races from 14 starts with Inter Europol Competition and TS Corse to claim the championship title, becoming the series' final ever champion.
Financial pressure hampered 2019 and 2020. Varrone contested three rounds of the BRDC British Formula 3 Championship with Hillspeed in 2019, winning a reversed-grid race at Spa-Francorchamps, and signed with Chris Dittmann Racing for 2020. The COVID-19 pandemic cut the season short after two rounds, and Varrone was forced to abandon his formula career.
Facing the prospect of leaving racing entirely to work in his family business, Varrone was connected with Rinaldi Racing through his manager Jose Balbiani. He tested an LMP3 car and contested the final round of the 2020 Le Mans Cup. In 2021, Rinaldi paired him with Alexander Mattschull for the full Le Mans Cup season, where three podiums earned third place overall in LMP3.
In 2022, Varrone made his IMSA SportsCar Championship debut, entering the Six Hours of The Glen in LMP3, and signed with the AWA team for 2023.
In January 2023, Varrone signed with Corvette Racing to contest the LMGTE Am class of the FIA World Endurance Championship, sharing a Chevrolet Corvette C8.R with Nicky Catsburg and Ben Keating. The trio had an outstanding season, winning three races including the LMGTE Am class at the 24 Hours of Le Mans — Varrone setting the fastest lap in that race — and claiming the overall LMGTE Am World Championship title. The result earned Varrone an FIA Gold ranking upgrade ahead of 2024.
Varrone made his LMP2 debut at the 2024 24 Hours of Le Mans, partnering Ben Barnicoat and gentleman driver François Perrodo. The trio won the LMP2 Pro-Am subclass despite lacking pace in the wet closing hours, with Varrone contributing by taking and extending the overall lead during the night stages. He thus became a two-time Le Mans class winner across two different categories in consecutive years. Beyond Le Mans in 2024, Varrone contested five rounds of the European Le Mans Series with AF Corse, scoring a podium at Spa-Francorchamps.
For 2025, Varrone stepped up to the Hypercar class, joining Proton Competition alongside Neel Jani and Nico Pino for a full WEC season, supplemented by IMSA commitments with Corvette Racing where race dates permitted.
In 2026, Varrone returned to single-seater racing by signing with Van Amersfoort Racing for the FIA Formula 2 Championship, adding an unusual late chapter to a career that had moved in the opposite direction to most drivers — from formula racing to sportscars and back again.