"The boards of Müller and Robert Wiseman Dairies PLC are pleased to announce that they have reached agreement on the terms of a recommended cash offer to be made by Müller Dairy UK Limited for the entire issued and to be issued ordinary share capital of Wiseman," they said in an official statement.
The offer, pitched at 390 pence per Wiseman share, values the whole group at £279.5 million (€338 million).
Robert Wiseman Dairies, which is based in Glasgow and runs seven dairies across Britain, said more than half its shareholders had already accepted the offer from the German-owned yoghurt maker.
The 5,000-employee firm had turnover of more than €1 billion in 2010 and supplies about a third of the United Kingdom's fresh milk.
Müller, which also employs roughly 5,000 employees, is best known for its wide range of yoghurt projects. It is based in the Bavarian town of Fischach.