Pressure for an operation to retake the town had grown in March after IS launched a chemical attack from Bashir on the nearby town of Taza that killed at least three children.
Kurdish peshmerga forces and Turkmen Shiites from the Popular Mobilisation units, a militia umbrella organisation, took part in the operation, officials said.
Peshmerga and Turkmen forces completed operations to recapture Bashir as well as several nearby villages, said Asso Mamand, an official from the Patriotic Union of Kurdistan Party.
Abu Ridha al-Najjar, a Turkmen Shiite commander, also confirmed that Bashir was recaptured, as did the Kurdistan Regional Security Council.