The 19-year-old has spent the summer on trial in the Championship club's development system.
Phillips was released by Liverpool in May after 10 years at the Anfield club, having joined as a nine-year-old from Blackburn.
"It's a great move for me and a great opportunity to come to a club like Norwich," said Phillips.
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Norwich City have signed former Liverpool youngster Adam Phillips on an initial two-year contract.