Eusèb Obrecht was likely born in the 1840s in Grenchen.
Obrecht established a watchmaking company in Grenchen in partnership with E. Kully in 1866. This was the first watchmaking operation in the town, and its success drew many others to settle there. The firm of Obrecht & Kully became one of the largest employers in the city in the 1870s. Kully appears to have died by 1883, when Obrecht is listed as the sole owner of Obrecht & Kully.
Obrecht also operated a watch sales business under the name E. Obrecht in Grenchen in the 1880s, though this was bankrupt in 1899. In 1883, Obrecht founded an ebauche factory there. Called Société d'Horlogerie de Granges, it was founded by Obrecht and Rudolf Zumstein-Girard.
Euseb Obrecht is no longer listed in association with Obrecht & Cie in 1919, suggesting that he had died.