The RB15's development was defined by the switch from Renault to Honda power, a change that necessitated a complete redesign of the car's rear end to accommodate the new unit. The Honda RA619H featured a split turbo system broadly comparable in concept to that used by Mercedes. Engineers also revised the cooling system, reworked the aerodynamic package — including wing design and bargeboards — and refined airflow throughout the chassis.
Pierre Gasly moved up from Toro Rosso to partner Verstappen, replacing Daniel Ricciardo who had departed for Renault. Gasly struggled to match Verstappen's pace and results from the outset: he was eliminated in Q1 at the opening race in Australia through a strategy error and was lapped by his team-mate at both Austria and Hungary. On 12 August 2019, Red Bull announced Gasly would swap back to Toro Rosso and be replaced by Alexander Albon with immediate effect from the Belgian Grand Prix.
The RB15 made its competitive debut at the 2019 Australian Grand Prix, where Verstappen finished third — Honda's first podium since 2008. Team principal Christian Horner praised Gasly over the radio for his recovery from 17th to 11th. Over the early rounds, Verstappen collected top-five finishes in Bahrain, China, Azerbaijan, and Spain, with Gasly generally in his shadow.
The defining moment of the season came in Austria. After a grid penalty moved Verstappen to the front row and he fell to eighth at the start after engaging anti-stall, he carved back through the field to win. It was the first Honda-powered Formula One victory since Jenson Button's win at the 2006 Hungarian Grand Prix in the Honda RA106, and the first non-Mercedes win of the 2019 season.
A second victory followed in Germany in a wet-to-dry race of attrition, where both Ferraris suffered power unit problems. Verstappen spun on lap 27 yet still came through to win for the seventh time in his Formula One career. At Hungary, he took the first pole position of his career, simultaneously becoming the first Dutchman to take an F1 pole and the 100th different polesitter in the championship's history since 1950. Mercedes strategy denied him victory but he finished second.
With Albon in the car, Red Bull continued to score points. Albon finished fifth on his team debut in Belgium and fourth in Japan — the best result of his Formula One career at that point. The season concluded with Verstappen's third win in Brazil; Albon had been running second until contact from Lewis Hamilton on the penultimate lap dropped him to 15th.
At Monaco, the team paid tribute to the recently deceased Niki Lauda by placing his image and the words "Danke Niki" on the sidepods. At Silverstone, both cars ran James Bond-themed liveries to mark the championship's 1007th World Championship race, with licence plate numbers on the rear wings referencing Aston Martin film cars from Goldfinger and The Living Daylights. At the British Grand Prix on lap 12, Red Bull also set a new Formula One pit stop record of 1.91 seconds during Gasly's stop, breaking the previous mark of 1.92 seconds jointly held with Williams since 2013.
The RB15 finished third in the Constructors' Championship behind Mercedes and Ferrari. Verstappen ended the Drivers' Championship third with three victories. A modified version of the RB15 was used to test the 2022 tyre compounds following the 2021 Abu Dhabi Grand Prix.