"The proposal happened a while ago," a source told the magazine. "She just didn't wear the ring."
"Of course they couldn't be happier to be engaged and are excited to share the rest of their lives together," another source told PEOPLE.
"Amber has really taken well to the kids and really enjoys spending time with them," added the source. "She's even taken Lily shopping on her own for some bonding time."
Amber caused a stir earlier this week when she was spotted wearing a large diamond on her ring finger.
The 27-year-old actress sparked speculation when she stepped out in LA this week to dine with a female friend at Ago restaurant.
As she left, Amber did everything she could to shield her left hand from photographers, even waiting for the valet driver to open the car door so she didn't have to show her finger, but for a brief moment, the ring appeared.
Johnny, 50, and Amber, who were first linked at the beginning of 2012, stepped out together as recently as Saturday, when they took their very private romance public at a star-studded gala.
Amber was previously in a four-year relationship with ex-girlfriend Tasya van Ree, while Johnny had a relationship with Vanessa Paradis, the mother of his two children, for 14 years.