"Tattoo" was laid down by William Beardmore and Company, Limited, at Dalmuir in Scotland on 21 December 1917. The destroyer was launched on 28 December 1918, and completed on 7 April 1919. The ship was commissioned into the Royal Navy in April 1919, but was quickly marked for transfer to the RAN, along with four sister ships. "Tattoo" was commissioned into the RAN on 27 January 1920. There were plans to rename her HMAS "Moresby", but these were cancelled in June 1930.