Stacy is the father of Gwen, the love interest of Spider-Man/Peter Parker in the film, which is to be directed by Marc Webb starting next month.
Emma Stone has been cast in the role of Gwen, while Andrew Garfield is to play the titular web-slinger.
Details of the movie's plot are being closely guarded, The Hollywood Reporter said.
Leary's film credits include "The Ref," "Two if By Sea," "The Matchmaker" and "The Thomas Crown Affair." He is also the star and co-creator of TV's "Rescue Me."
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