Becchio handed in a transfer request at Leeds last week after talks over a new deal for the Argentine faltered.
The 29-year-old, who scored 19 goals for Leeds this season, successfully underwent a medical at the Norfolk club this morning and joins Norwich on a three-and-a-half-year deal.
Becchio said: “I spoke to (former Leeds team-mates) 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.”
Norwich have given Leeds Morison in return and paid a further undisclosed sum in order to bring Becchio to the club.
Morison, 29, has also signed a three-and-a-half-year deal to bring to an end an 18-month stay at Norwich that saw him score 10 goals in 53 league games.
Leeds manager Neil Warnock said: "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."
Norwich are also expected to sign Kansas City striker Kei Kamara and have been further reported to have made a fourth offer for Celtic striker Gary Hooper.