In 1980 Lancia began designing the 037 to comply with the then new FIA Group B regulations that allowed cars to race with relatively few homologation models being built. As the project was number 037, this eventually became the name by which the car was known. Abarth, now a part of the Lancia-Fiat family, did most of the design work, even incorporating styling cues from some of its famous race cars of the 1950s and 1960s such as a double bubble roof line. The car was born from the collaboration between Pininfarina, Abarth, Dallara and the project manager, engineer Sergio Limone. Prior to its first participation in the 1982 World Rally Championship season, 200 road-going models were built to comply with Group B regulations.

The car made its competition debut at the 1982 Rally Costa Smeralda in Italy, where two cars were entered but both retired due to gearbox issues. The 1982 season was plagued with retirements for the 037, but the new car did manage to achieve several wins including its first win at the Pace Rally in the UK. The 1983 season was considerably more successful for the 037: Lancia took the 1983 World Rally Championship Constructors' title with Germany's Walter Röhrl and Finland's Markku Alen its principal drivers, despite serious competition from the 4WD Audi Quattro. Both drivers, however, missed the final round of the series, despite Röhrl maintaining a mathematical chance of the drivers' title: such honours instead went to Audi's veteran Finn, Hannu Mikkola.