The deal sees striker Steve Morison head the other way as part of a swap.
"I spoke to Snodgrass and Howson about Norwich and they both had really good things to say about the club and the city," Becchio told the club's official website.
"I cannot wait to play my first game for Norwich. I am really happy about having the chance to play in the Premier League, it is brilliant for me personally and for my career."
Becchio scored 75 league goals in five years at Elland Road.