ABG has struck a deal to buy the 35-year-old company for £211 million ($254 million).
Like other bricks-and-mortar businesses, Ted Baker has struggled in the face of fierce online competition before and during the Covid pandemic.
"Ted Baker is a highly regarded, uniquely British brand whose strong fashion credibility resonates with consumers around the world," ABG chief executive Jamie Salter said in a statement.
"We are excited to build on the brand's global foundation through a business model focused on licensing, wholesale, retail, digital and strategic marketing partnerships."
Ted Baker shares surged 17 percent in London deals in a move that reflected the offer price.