The Dutch international spent last season on loan at French side St Etienne, where he scored five times in 18 league starts.
His only appearance for Norwich this season came in their 2-1 League Cup win over Rotherham United on Aug. 25, where he scored the winner to send the Canaries through to the third round.
Wolfswinkel is the third player to leave Norwich in the current transfer window, following Cameron McGeehan and Mark Bunn, and joins a Betis side that currently sit 18th in La Liga, where they have one point from two games.
His exit follows Monday's arrival of Democratic Republic of Congo international striker Dieumerci Mbokani on a season-long loan from Ukrainian club Dynamo Kiev.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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