Under the brief, which will run for a minimum of two years and is worth an annual six-figure sum, Cirkle will also work on recently acquired Nomad brand Goodfella's Pizza.
At the start of the year, Birds Eye announced a new campaign to modernise and reposition its brand and the captain himself.
Cirkle's work begins in August, led by senior director Kate Gibson.
Mischief, which previously held the account, declined to repitch.
Cirkle's new MD Ruth Kieran said: "The food industry is under increasing scrutiny around food provenance, sustainability and health, making the frozen food sector and Birds Eye's quality proposition even more relevant to today’s demanding consumer.
"We look forward to inspiring consumers to extend their frozen food repertoire by providing them with fresh food when they need it with less risk of waste - and to helping Birds Eye meet its ambitious targets."
Ingenuity, the new business consultancy, assisted Birds Eye with agency selection.
Nomad Foods also recently acquired Aunt Bessie's, the maker of Yorkshire puddings and other frozen fare, for £210m.