Just a few weeks after the newfound couple were spotted out and about together, a source now tells ET that the two have "gotten serious, quickly."
"[They] went from casually dating to spending much more time together," the source says. "Chris and Katherine have introduced one another to their family and friends, and have been almost inseparable when they are free."
According to our source, Schwarzenegger (the daughter of Arnold Schwarzenegger and Maria Shriver) has even "spent quality time" with Pratt's 5-year-old son, Jack, whom he shares with his ex-wife, Anna Faris.
"That was a big step for Chris," the source adds. "Until he knew it was more than just casual, he wasn't introducing Jack to anyone. Chris and Katherine are very happy together."
Pratt, 39, and Schwarzenegger, 28, were first seen together in June, on a casual picnic in Santa Barbara, California. Since then, the two haven't been shy about showing their affection toward one another in public.
Over the weekend, photographers snapped pics of the actor and his lady locking lips while enjoying some ice cream in Los Angeles.