The 18-year-old, who can play up front or on the wing, is expected to go straight into manager Greg Abbott's squad for Saturday's home game against Coventry.
"Adam is a good young player who has been right on the fringes of the Newcastle United first team," Abbott told the club's official website.
"I spoke with Alan (Pardew) about him and he thinks a heck of a lot of him. He's at a stage of the season where he wants Adam to get more football and he knows that we look after players like this.
"We have a really good relationship with Newcastle and Alan knows that we are after numbers to help our squad at the moment.
"Hopefully this is one of those that will work out for all parties because there is no doubt that we are getting a good player who has a bright future ahead of him."
Campbell, who has represented England at Under 16 and 17 level, made his senior debut for Newcastle in the Europa League fourth qualifying round tie at Atrmitos in August 2012 and has made three Barclays Premier League appearances.