Craig, 22, has signed with the Eagles for an undisclosed fee on a three-year-deal.
The left-back has been Millwall's young player of the season for the past two years.
"It's a nice step up for me," Craig said. "I've played in the Championship before with Millwall and I'm thoroughly looking forward to it.
"Hopefully we're looking to get in the play-offs - we all want a good season."