Campos, who will report to the executive creative director, George Prest, has been a digital creative director at Fallon since April last year, working on accounts such as Orange and Cadbury.
Before Fallon, Campos was a design director at Glue London working on Bacardi, Toyota and Sony.
In the past, he has worked as a senior art director at Curious Group on clients including Dell and Adidas.
Unilever appointed R/GA as its global digital agency of record for its Rexona brand, known as Sure in the UK, in February. R/GA also works on other Unilever brands including Magnum, PG Tips and Marmite.
Prest said: "Raphael is a proven operator on both sides of the traditional/digital landscape. He's just the sort of person we need to help us drive our Unilever business forward."