Parker joins as a director after nearly six years at the supermarket, where he was corporate comms manager.
He reports to head of corporate comms Nick Bishop as the agency seeks to continue expanding the practice, which it claims has doubled in revenue over the past year.
"Our clients told us they wanted world-class media strategy and outstanding senior relationships. That’s exactly what Tom brings," said Bishop.
"His experience in a major UK corporate is invaluable to our clients and what he adds in terms of developing our talented young team is second to none."
Parker was at Eurostar before joining Sainsbury’s as a press officer in 2008.