The 23-year-old has also extended his contract with the newly-promoted Premier League Canaries until 2021.
Morris spent time on loan with the Millers in 2017, playing eight times.
"It's a great opportunity for me and I'm just really looking forward to getting started," Morris told the Norwich club website.
"I really enjoyed my time there in 2017 and it's a great club. I get on with the manager [Paul Warne] really well and I know most of the lads so have already built those great relationships."
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