The pair join from Fallon, where they held an equivalent role, and will be responsible for working across the agency's client base and building its creative department.
They will work with the Beta founder, Robert Campbell, and will become shareholders in the business.
Cockrell and Storey began their career at Cogent London, moving on to DMB&B, Lowe Howard-Spink and then Simons Palmer Denton Clemmow & Johnson in 1994, where they worked on the launch of Sony PlayStation.
Three years later, the pair were hired by Campbell at Rainey Kelly Campbell Roalfe/Y&R, where they worked for six years before being hired by Abbott Mead Vickers BBDO to work on BT and Camelot.
They left in 2006 to join Fallon, where they worked on award-winning campaigns for Asda, Orange and Sony, including the latter's "Bravia-drome" starring the Brazilian footballer Kaká.
Cockrell said: "The opportunity to work with Robert once again was simply too good to turn down and we're looking forward to helping shape the agency's growth and creative direction over what promises to be a very exciting next few years."