The 18-year-old left RB Leipzig last month, having joined the Bundesliga side from his hometown club, Nottingham Forest, in the summer of 2018.
He has played for England at under-15, under-16, under-17 and under-18 level, and had a loan spell with Dutch side FC Dordrecht in the first half of this season, making seven first-team appearances for the Eerste Divisie club.
Left-back Bondswell will initially be part of Chris Hogg and Peter Ramage's under-23 squad.
"It's an amazing feeling to be at such a big club," he told nufc.co.uk. "I'm really looking forward to getting started with the boys and hopefully doing some successful things in the future."