Leeds' 29-year-old Argentinian Becchio signed on the dotted line, penning a three-and-a-half-year deal that involved Steve Morison heading in the opposite direction.
Kei Kamara also joined the Canaries on loan from Sporting Kansas City.
"I want to thank the Norwich manager for giving me this chance," said Becchio.
"I want to pay him back for all the sacrifice and effort he put in to getting me this move."
The former Barcelona B forward enjoyed almost unanimous support during his four-and-a-half-year stay with United, scoring 86 goals after arriving as a complete unknown.
He left the club as one of their top 10 leading goalscorers of all time.
"The years I spent at Leeds were the most marvellous, and until today, the happiest of my career. I will carry the affection and love of the Leeds fans in my heart," Becchio said.