A source told US Weekly magazine: "They are living together now," and are "totally inseparable."
The blissfully happy couple are said to be joined at the hip but are in no rush to wed, as they have both been married before.
'Saturday Night Live' star Jason was previously married to actress and '30 Rock' writer Kay Cannon from 2004 to 2010.
Olivia divorced her husband of eight years Italian American filmmaker and musician Tao Ruspoli in September 2011.
The source said: "They've both been married, so they've already experienced that and know what it entails. It's something for down the road."
The couple always make time for romantic dates despite their hectic schedules.
The 37-year-old actor snuck away from the 'Saturday Night Live' set to take her to a concert in New York City last week.
The source said: "Everyone on the show staff was writing late, but Jason managed to sneak over to Radio City Music Hall to see Bon Iver with Olivia."
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