An arbitrator has ruled that a former Boston police officer who was acquitted on charges of being an accessory to a 2005 slaying was unjustly fired after a department investigation into the matter and ordered him reinstated with back pay.

In a 36-page decision dated ­July 19, independent arbitrator Richard G. Boulanger ruled for Baltazar ­DaRosa, 34, who had been terminated by the Police Depart­ment in 2010. Boulanger is an ­arbitrator ­approved by the patrolmen’s union and the city to hear disciplinary appeals.