EDP works primarily on spa interiors and has been active across the Middle East since 2005.
Glasgow based Barr + Wray, which has previously worked with EDP, said the move will allow it to offer a more integrated spa design and delivery offering.
Alister MacDonald, managing director, said: "In recent years, we have seen a growth in enquiries for spa interior design services from the Middle East region and this move is a demonstration of our commitment to meeting our customers' needs while growing the business."
EDP's three designers are transferring across as part of the deal.
Earlier this year Barr + Wray said its growth in the Middle East was a factor in profits rising to £1.3 million.