The 22-year-old has been with the Canaries since the age of 10, but he is yet to make a senior appearance for the club.
Speaking to Doncaster's official website, Matthews admitted that the chance to play under Darren Ferguson's management was too tempting to reject.
"I knew straight away I wanted to come here. I wanted to play for Darren Ferguson, he's a big name in football with a good reputation," he said.
"I can see straight away that he has faith in me, and that's a great opportunity for me on the field as well as to work alongside him."
Matthews had a loan stint with Burton Albion earlier this term.