Advent is offering €38 per share for all outstanding shares in the publicly-listed retailer, Douglas said in a statement.
With €39.4 million shares in issue that would value the company at €1.497 billion.
Douglas said the group's three main family shareholders - Oetker with 25.8 percent, Kreke with 12.78 percent and Müller with 10.8 percent - had all agreed to accept the offer and Advent so far had assurances for at least 50.5 percent of the company's share capital.
Upon completion of the takeover, the Kreke family would then take a 20 percent stake in the investment vehicle making the offer, Beauty Holding Three AG, with the other 80 percent held by investment funds operated by Advent International.
"This takeover offer is based on the mutual intent of the Douglas founders, the Kreke family, and Advent International to fine-tune and implement a successful long strategy for the Douglas group," the statement said.
Douglas, which also sells jewellery, chocolates and books, has annual sales of more than €3.0 billion and operates a network of some 2,000 stores across Europe.