The Argentinian striker has signed a three-and-a-half-year deal and joins former Leeds team-mates Robert Snodgrass, Jonny Howson and Bradley Johnson at Carrow Road.
Becchio, who spent five-and-a-half years at Elland Road and is Leeds' top scorer this season, told the City website: "I cannot wait to play my first game for Norwich.
"I spoke to Robert Snodgrass and Jonny Howson about Norwich and they both had really good things to say about the club and the city.
"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."
Morison, meanwhile, makes the move north after struggling to hold down a first-team place this season.
The 29-year-old, who arrived from Millwall in the summer of 2011, scored 12 goals in 85 appearances for Norwich.
Leeds boss Neil Warnock admitted he was thrilled to get his man: "I'm absolutely delighted that we've been able to bring Steve in.
"Even before Luciano put in his transfer request we had enquired about Steve - he was at the top of my list in January to bring in - and I can't tell you how delighted I am.
"Steve meets all the requirements of the striker we've been looking to bring in. For me, he is a player who has everything. He can score goals from anywhere - whether it's 25 yards or a tap-in - he has pace, and he has all the attributes you want."