The American Horror Story star, 29, revealed the news in a series of snaps on Instagram.
In one image she is seen cradling her belly, while another shows her with her partner Garrett Hedlund.
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Roberts wrote of Hedlund and the soon-to-be new arrival, “Me…and my two favourite guys,” confirming she is expecting a boy.
Roberts is the niece of actress Julia Roberts and previously dated actor Evan Peters.
Hedlund, who was previously in a relationship with Kirsten Dunst, is also an actor and starred in Netflix film Mudbound.
