The midfielder was involved in a deadline day signing that saw his time with the Canaries come to an end, making the move to the Championship club on a loan deal.
"It is something I wanted to get done. I wanted to get out and as soon as I knew it was a possibility it was a pretty easy option for me," he told the Bournemouth club website.
"The manager (Scott Parker) said everything that made me think this is definitely the right move for me. I like the direction the club is moving in and we both want success."
Cantwell had only been used eight times throughout the season in the Premier League by Norwich, struggling for game time throughout the campaign, which is why the club were happy to let him go.
The 23-year-old could be set to make his debut for the Cherries on Sunday when they face Boreham Wood in the FA Cup.