The deal, worth up to £500,000 with half of that upfront, sees Minoan enter the potentially lucrative corporate travel market in Aberdeen.
Duncan Wilson, Minoan managing director, said: "We are delighted to have completed this acquisition and to have established a presence on the ground in Aberdeen in order to build on the Group's initial success in possibly the most vibrant business travel market in the UK."
Minoan has snapped up a number of Scottish travel businesses in recent years but has consolidated many of them under the Stewart Travel brand. It expects the deal for Martin Singer to be earnings enhancing in its first year. Shares closed up 0.38p to 14.75p.