The "My Big Fat Wedding" star will recur as a political consultant, Annie Spiro, on the series starring Nick Nolte and Sela Ward, said The Hollywood Reporter.
Vardalos, 53, takes on the role after producers and Anne Heche could not reach a deal for the part.
Picked up straight-to-series, the single-camera comedy stars Nolte as a former president of the US.
Two decades after his term ends, he begins to think that his policies have damaged the country for decades, so he goes on a Don Quixote-like journey to fix things.
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Vardalos' Annie Spiro will be a woman with a killer instinct who is hired to manage Graves' potential Senate campaign.
The duo share a history, Graves gave Spiro her first job and despite their bond, the latter has to understand that former's first loyalty is to her husband.
Production is under way in New Mexico on the 10-episode series, which was delayed a few weeks during the search to replace Sarandon.
Joshua Michael Stern (Swing Vote) created the comedy and will write, direct and executive produce the series. Oscar-winning producer Greg Shapiro (The Hurt Locker) also executive produces.