The £1bn acquisition, which was announced on 11 March, had already received approval from China's Ministry of Commerce and the US Federal Trade Commission.
Domino will now hold a court meeting on 4 June at which it will seek approval from shareholders representing at least 75% of Domino's shares by value.
Subject to successfully gaining shareholder approval, Brother and Domino expect the deal to go through on or before 11 June.
Brother is currently exhibiting at Fespa 2015 in Cologne, where it showing products including its GT-3 series direct-to-garment printer.