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The couple have been together for more than four years.
They costarred in 2003's In God's Hands, a low-budget feature produced by Steven Soderbergh that was never released.
Gyllenhaal, 28, has appeared in more than 20 films, including Secretary, Mona Lisa Smile and Donnie Darko, which starred her brother, Jake Gyllenhaal.
Sarsgaard, 35, has also shared the screen with his fiancée's brother – in last year's war film Jarhead. Sarsgaard's résumé includes Boys Don't Cry, Kinsey and Shattered Glass, for which he earned a Golden Globe nomination in 2004.
This will be the first marriage and first child for both actors.
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
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