Both sides said the deal will help Ren, which takes its name from the Swedish word for clean, to the next stage of global growth.
Vasiliki Petrou, the senior vice-president of Unilever’s Prestige Brands division, said: "Ren is a brand with an incredibly loyal following, with a unique proposition that no doubt gives it potential for even further growth."
The brand is sold in 50 countries. Last year it hired ad agency Lucky Generals to launch the brand in Scandinavia.
Antony Buc, the Ren chief executive who co-founded the brand in 2000 with Robert Calcraft, described Unilever as "the perfect partner to help Ren fulfil its future potential worldwide".
In the UK, Ren is stocked by Liberty, Space NK, John Lewis, Marks & Spencer, Asos and selected independent retailers.
Unilever's personal care portfolio includes Dove, Simple, Vaseline and Pond's.