Born on 31 August 1991 in Cascais, Portugal, Félix da Costa moved through karting and Formula Renault 2.0 before spending three seasons in the Formula 3 Euro Series and the GP3 Series. By 2012 he was competing across multiple championships simultaneously and was fast-tracked into the Formula Renault 3.5 Series mid-season by the Red Bull Junior Team following a strong display in GP3.
Midway through the 2012 Formula Renault 3.5 season, Félix da Costa was selected to replace Lewis Williamson at the Arden Caterham team — Williamson had failed to score a point in the first three rounds. Félix da Costa joined from the fourth round at the Nürburgring and made an immediate impression.
He scored a first podium at Silverstone when he converted a ninth-place grid start into second place, and then took his maiden series victory at the Hungaroring in the second race of that weekend, benefiting from race leader Kevin Magnussen's engine failure on the final lap. He followed this with a victory in a rain-affected opener at Le Castellet and a double win in the season-closing rounds at Catalunya, winning the first race by passing championship contender Sam Bird and the second by almost 28 seconds in wet conditions. Despite missing the first five rounds of the season, Félix da Costa finished fourth in the championship with 166 points, just 23 points behind champion Robin Frijns.
His performances attracted the attention of Red Bull Racing, who invited him to their Young Drivers' Test in Abu Dhabi. Félix da Costa set the second-fastest time on day one and topped the timing sheets on day two, recording a lap half a second quicker than the next best driver.
Félix da Costa remained with Arden Caterham for the 2013 season, his first full campaign in the series. He was identified by 2012 champion Robin Frijns and others as one of the leading championship contenders alongside Kevin Magnussen.
Félix da Costa's runs in the Formula Renault 3.5 Series announced him to the wider motorsport community and confirmed the potential he had shown in Formula Three and GP3. He went on to win the Macau Grand Prix for a second time in 2016, becoming only the second driver to win the iconic street race on multiple occasions in the modern era. He won the 2019–20 Formula E Championship with DS Techeetah, securing the Drivers' and Constructors' titles simultaneously with dominant performances at the season-closing Berlin rounds. In endurance racing, Félix da Costa won the FIA Endurance Trophy for LMP2 Drivers in 2022 with Jota. His Formula Renault 3.5 campaigns, particularly the explosive entry in 2012, were the inflection point that demonstrated he could compete and win against established contemporaries at the top of the European junior ladder.