The PRWeek UK Top 150-listed agency Salt had collaborated with creative group MullenLowe for the past decade on mutual clients, and was then acquired for an undisclosed sum last month.
MullenLowe PR in the US will also handle the brief, which will see a creative campaign rolled out across different international markets on a staggered basis over the next three years.
Fellow Interpublic Group-owned PR firm Weber Shandwick's US PR contract with Rexona is not affected.
Alex Leikikh, MullenLowe Group's global CEO, said: "Rexona is a brand with ambitions to drive positive change. Our PR team helps brands penetrate into cultural conversations with content that drives affinity, loyalty and action. This is a perfect partnership of brand purpose and agency capability."
Salt had worked on other Unilever deodorant brands for several years, while MullenLowe PR in the US first worked with Unilever last year. Other MullenLowe PR clients have included low-cost airline JetBlue and greetings card firm American Greetings.
Rexona is one of 13 Unilever brands with sales of $1bn (£769m) for 2016, according to Unilever's latest annual report. Others include Hellmann's, Axe, Dove, Surf and Magnum.