The creative directors Storey and Cockrell will join as creative editors, sitting between the agency's recently hired joint creative directors, Paul Belford and Nigel Roberts, and the rest of AMV's creative teams.
The pair are Belford and Roberts' first hiring since taking over the creative helm in March, following the departure of the long-serving creative director, Tony Cox.
Belford said: "Graham and Phil have, over the years, consistently produced and overseen excellent work for big clients. On top of that, they are thoroughly decent blokes. I am convinced they will fit in brilliantly."
Storey and Cockrell joined RKCR/Y&R in 1997 as a senior team to provide back-up for the agency's then creative directors, Robert Campbell and Mark Roalfe.
They worked on the agency's Virgin Atlantic, Toblerone, Scottish Courage and News International accounts before stepping up to the position of creative directors, along with Pip Bishop and Chris Hodgkiss, in 2001.
This move followed Campbell and Roalfe's promotion to the agency's executive creative directors.
Before 1997, the pair worked at Simons Palmer Denton Clemmow Johnson, where they won a gold Lion for their Nike "marathon" poster.
They also worked on the "society against PlayStation" pitch-winning idea that secured the Sony account for the agency.
Storey and Cockrell have also worked at DMB&B and Lowe. They join AMV in July.