In the sweet snapshot, Olivia is pictured cradling her newborn son close and smiling with her eyes closed. The bundle of joy is wrapped up in a blanket and nestled into his mother’s chest, with his face hidden from view.
The image caused a stir on Twitter and was retweeted more than 4,000 times in less than four hours.
This is the first child for Olivia and Jason, who announced that they were expecting a child last October.
The Rush actress confirmed early on that she was having a boy, and hinted at the 2014 Golden Globes that her due date was on 4 May, as she told Ryan Seacrest, "May the fourth be with you!" when probed.
Olivia and Jason, who have been dating since November 2011, got engaged in January 2013.