The agency was appointed following a pitch against Grey and two other agencies, and has been briefed to develop a campaign that will extend the brand's appeal beyond swimwear to include its full range of sportswear.
The campaign will run across the company's key markets in Europe, the US, Japan and Australia.
Fallon was retained on Speedo's pan-European account between 2002 and 2004, but the company's communications over these two years were handled in-house.
The pitch was led by Speedo's new brand president, Tony Wood, who joined from Speedo's sister company, Berghaus, in December.
He said: "Speedo is distributed in 176 countries worldwide and, therefore, our challenge is to roll out a consistent brand message to consumers globally.
The DDB team delivers innovative brand solutions. I'm confident the Speedo and DDB teams will meet this objective."
Richard Morris, the business development director at DDB, added: "Speedo has the most fantastic Olympic history, great product stories and stand-out design."