The brand, which has a UK sales value of £43.8m, would benefit from a host of "exciting brand-building" activity, claimed John Hyman, sales director at First Drinks.
Incorporating Tia Maria would increase its total portfolio's value 11.6% to £424m, said Hyman, and it would "perfectly complement" its other non-cream liqueurs Disarrono and Cointreau.
"We will be giving strong above-the-line marketing support to these three leading non-cream liqueur brands over the next 12 months," he said.
First Drinks was working with Tia Maria's previous distributer, Pernod Ricard, to guarantee a smooth handover on 1 October, he added.
Italian spirit producer Illva Saronno bought Tia Maria from Pernod in July.