A source told the news magazine, "Of course they couldn't be happier to be engaged and excited to share the rest of their lives together. Amber has really taken well to the kids and really enjoys spending time with them. And she's even taken Lily shopping on her own for some bonding time."
Depp, 50, has two children -- son Jack and daughter Lily-Rose -- from a previous relationship with Vanessa Paradis. The couple split in 2012 after 14 years together.
At the time of the breakup, Depp told Rolling Stone, "The last couple years have been a bit bumpy. At times, certainly unpleasant, but that's the nature of breakups, I guess, especially when there are kiddies involved."
Heard, 27, starred alongside Depp on his 2011 passion project The Rum Diary, where the two first met. The couple will be sharing the screen again in London Fields, out later this year.