Argentinian forward Becchio, who has scored 19 goals for Leeds this season, handed in a transfer request at Elland Road last week after talks over a new deal faltered. Norwich hope the deal will be completed in time for Becchio, 29, to feature at QPR on Saturday.
A club statement read: "Becchio has agreed a three-and-a-half year deal with the Canaries' ending a five-and-a-half year stint at the Yorkshire club, joining fellow former Leeds men Jonny Howson, Robert Snodgrass and Bradley Johnson in the City ranks."
Former Boca Juniors player Becchio feels he is ready to make the step up to the challenges of the English top flight.
He told Canaries Player: "I am really happy about having the chance to play in the Premier League, it is brilliant for me personally and for my career.
"The Premier League has some brilliant players including people like (Sergio) Aguero and (Carlos) Tevez (Becchio's compatriots) and it will be a great experience for me to play against players of that quality."
Wales striker Morison, meanwhile, will look to kickstart his career with Leeds after falling down the pecking order at Norwich after his £2.8million move in the summer of 2011.
Norwich, who drew 1-1 at home with Tottenham on Wednesday night, have been on the look-out for a striker all month to help them in their bid to avoid a slump in form which has seen them drop to within seven points of the relegation zone.
The Norfolk club, who have had several bids for Celtic striker Gary Hooper rejected, have only scored 25 league goals in 24 matches so far this term.
Norwich confirmed on Wednesday they had signed striker Kei Kamara on loan from Sporting Kansas City, subject to him receiving a work permit. The Sierra Leone international has since tweeted: "Am so excited for this opportunity to play for @NorwichCityFC. i cant wait to get out there, see everyone and feel the energy @ Carrow Road."
Source: PA
Source: PA