The 22-year-old Englishman will spend a season on loan with Accies in the Scottish Premiership.
He becomes Accies' second signing of this week after the arrival of full-back Jack Breslin, released by Celtic.
Former manager Alex Neil, now Canaries boss, said: "Remi needs to go out and get some games."
Matthews has already had two loan spells with Burton Albion and ended last season playing nine times for Doncaster Rovers in England's League One.
"He'll go up to Hamilton and hopefully get a good season under his belt," said Neil.
"You've got Celtic and now Rangers in that league, so it will be really competitive for him."
Matthews, whose new deal with the English Championship club includes with the option of a further 12 months, arrives at New Douglas Park as McGovern considers his options after rejecting a new contract amid fresh offers following his fine performances at Euro 2016.
He will make his debut as Accies kick-off their season with a Scottish League Cup tie away to Ayr United on Saturday.
"It's always nice to have that security behind me, so to have another year under my belt is a positive step," Matthews told Norwich's website.
"I was out on loan twice last year and felt like I was improving with every game, so I'm looking to build on that and show everyone what I can do."
Breslin has signed a permanent deal with Accies from Celtic after the 19-year-old played seven times in his second loan spell with Annan Athletic in League Two.
Accies player-manager Martin Canning had already added to his defensive options by signing centre-half Jordan McGregor after the 19-year-old was released by Hibernian after a loan spell with Berwick Rangers.
Remi Matthews has joined Hamilton as a replacement for Northern Ireland keeper Michael McGovern after signing a new two-year contract with Norwich City.