The game was produced under Sony's long-running Formula One license and developed jointly by Studio 33 and Studio Liverpool, with many employees from former franchise owner Psygnosis contributing to the project. Development peaked at around 25 people, the majority of whom were programmers and artists. The game's engine was built on a research and development project that had begun two years before the game's release, targeting physics simulation, collision modeling, and AI behavior.
Sony assembled an extensive reference library for track recreation, including aerial photographs, close-up circuit photography, and more than 200 hours of race footage sourced from F1 Digital+. The PlayStation 2's processing capabilities allowed the team to render trackside details that had previously been omitted and to create unique cockpit camera angles. Audio samples for all the cars were sourced directly from Formula One Administration, with additional recording sessions at Jordan and Prost garages conducted by sound engineer Michael de Belle.
Formula One 2001 covers the full 2001 Formula One World Championship with all teams, drivers, and circuits from the season, with some exceptions. Tarso Marques appears in the game but is never identified by name in commentary. Replacement drivers Ricardo Zonta, Alex Yoong, and Tomáš Enge are not featured. The Panasonic Toyota Racing team, which unveiled its car during the 2001 season, is also absent.
The arcade mode followed the structure established in Formula One 2000, with upgrades to the player's car offered as incentives. A new Challenge mode placed the player in Jenson Button's Benetton B201 for a timed lap around Spa-Francorchamps, with fast lap times rewarded with a verification code and the ability to compare times online.
The European and North American versions of the game differ in their driver rosters to reflect mid-season changes: in the European release Jean Alesi drives for Prost and Heinz-Harald Frentzen for Jordan, while the North American version — released in October — reflects the later switch between the two drivers. Similarly, Luciano Burti is listed at Jaguar in the European version and at Prost in the North American version.
Some editions of the game included a bonus DVD offering a commentated, race-by-race review of the 2000 Formula One World Championship. The DVD allowed viewers to toggle between the main broadcast feed, an onboard camera, pit lane footage, and on-screen data such as lap times and positions — features derived from F1 Digital+'s original interactive pay-per-view coverage.
Sony mounted a significant promotional campaign around the game in the United States, centered on the 2001 United States Grand Prix. Jenson Button participated in a public event called the Formula One 2001 American Challenge on 29 September 2001 in Castleton, Indiana. The event was a time trial competition in which Button raced against consumer finalist Chris Ohanian, who had qualified by posting one of the top two times in a preceding competition. Button won with a lap time of 1:15.6 against Ohanian's 1:16.0. The broader campaign included national television advertising across network, cable, and syndicated sports programming, along with print and online promotion.
The PlayStation 2 version of Formula One 2001 received average reviews according to Metacritic. In Japan, Famitsu awarded it a score of 27 out of 40. The game was regarded as a competent official entry in the series, though it did not significantly advance the Formula One simulation genre on the platform.
Formula One 2001 marked the end of a significant stretch of North American distribution for Sony's Formula One franchise. No further entries in the series were released in North America until Formula One Championship Edition arrived years later, leaving a long gap in the North American market for officially licensed Formula One games from the Sony stable.