Becchio handed in a transfer request at Leeds last week after talks over a new deal for the Argentinian faltered.
Press Association Sport understands the 29-year-old, who has scored 19 goals for Leeds this season, successfully underwent a medical at the Norfolk club this morning and will sign for Chris Hughton's side this afternoon.
It is understood Norwich will announce the deal at around 1pm this afternoon.
Becchio joined Leeds from Merida in 2008 and helped the Yorkshire club gain promotion to the npower Championship the following campaign.
He went on to score 39 goals in the second tier of English football over the next two years, alerting a number of Premier League clubs to his talents in the process.
The Canaries 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 three bids for Celtic striker Gary Hooper rejected, have only scored 25 league goals in 24 matches so far this term.
The Sierra Leone international tweeted today: "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."