Canos impressed on loan at Brentford last season, scoring seven times, and on his return to Anfield made his Liverpool debut in the final Premier League match of the season at West Brom.
However, the Spaniard wanted more first-team football and after entering the final year of his contract he turned down a new deal from the Reds.
Bristol City, Fulham and Brentford were also interested in the 19-year-old but he opted for Carrow Road and has agreed a four-year deal.
“From the beginning, Norwich showed very good interest and showed that they believe in me,” Canos told Norwich City TV.
“I’m very excited to be here. Carrow Road impressed me, I’ve seen videos of it and it looks an amazing atmosphere and I can’t wait to play there.”
Canaries boss Alex Neil hopes the youngster can help fill the boots of Nathan Redmond, who was sold to Southampton.
“Sergi has a good background having been at Barcelona before moving to Liverpool at a young age,” he said.
“With Nathan Redmond leaving we wanted to replace him with someone exciting; someone who can dribble, can score goals and can provide assists.
“Hopefully Sergi can show everybody how good he can be.”