The 19-year-old defender, who was on loan at Bundesliga side FC Schalke 04 from South African club Bidvest Wits for two years, was out of contract in June but will link with United's under-23 squad after completing a successful trial with the Magpies.
The teenage centre-back, a representative of South Africa at under-20 level, attracted strong interest from a number of Premier League clubs and could be in line to make his young Magpies debut on Monday afternoon as United's second-string host Fulham at St. James' Park in Premier League 2.
"I'm very excited to be joining Newcastle United," Cross told nufc.co.uk. "I know it's one of the biggest clubs in England with its history and it's always been a dream of mine to play in the UK. It is an amazing achievement for me.
"I've spoken to the coach (Chris Hogg) and he's spoken of the ideas he has for me. I feel like I bring something different to the team and the coach encourages me to play to my strengths, which is something that has been very helpful. There is also a pathway to try and get into the first-team.
"I'm a left footed centre-back that loves playing football. I like when the ball is at my feet and love playing out from the back, looking for those window passes to break the lines.
"I want to help the team out as much as possible and just leave all I have out there on the pitch, giving 100 per cent for every game and training session."
Chris Hogg, Newcastle United's lead player development coach for the club's under-23 side, said: "We're looking to bring Brad in to try and add depth to the squad. He's played at Bidvest in South Africa and spent some time at Schalke most recently and I've had some good feedback on him during his time in Germany.
"It's an option where we looked at to bring in a left-footed defender and add some quality to the group but also to try and enhance the environment on a personal level too.
"He's a well-rounded character who made a good impression with everyone in terms of how he has behaved and how he conducts himself. We want people here who want to work hard and do things right so, from our point of view, we're delighted to have him and look forward to developing his game and seeing how far we can take him."