The move for the Glasgow-based firm is its third buyout in just the past four years.
EFR says the deal places it in the UK’s top 40 corporate travel providers.
WD offers a full service corporate travel management service with clients from across shipping, advertising, entertainment and IT.
Edward Rom, EFR founder and chief executive, said: “We look forward to working with [the WD team] to build up their very successful business still further.
“With their established client base and Scottish heritage, they complement our existing corporate travel businesses, EFR Corporate Travel and CSR Travel, perfectly.”