The agency will initially create TV, print and online advertising to promote the company's haircare division.
The ads will run in Europe and some other international markets, excluding the US. The first campaign, targeting young women, is expected to break in the autumn.
Last year, Remington parted company with its previous agency, Grey Worldwide, which had held the shaving and haircare global account for more than a decade. Grey declined to repitch.
The agency's last high-profile campaign for the brand broke in 2006. Using the endline "It's what's on the outside that counts", it controversially suggested the better you look, the more successful you will be in life.
Sally Sidani, Remington's European marketing director, said: "We knew we wanted to work with a new kind of agency, and were really impressed by the depth of expertise and quality of thinking Albion is able to offer."
MediaCom retains media planning and buying.