Pukki has played for Bundesliga side Schalke 04 and Scottish giants Celtic among other European teams.
"We got the feeling that Teemu is a good fit to our ideas because he is a technical player with really smart movements," Norwich manager Daniel Farke told the club's website.
"He also has lots of speed which is also important. Wherever he plays, he was always able to be there with goals and assists."
Pukki is Norwich's third signing of the transfer window following midfielder Moritz Leitner and playmaker Emi Buendia.
Norwich finished 14th in the Championship last season.
(Reporting by Aditi Prakash in Bengaluru; Editing by Ken Ferris)
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