Leeds will also receive a fee for Wales international Morison, 29, who signed a three-and-a-half year contract after quickly agreeing to join Neil Warnock's promotion challenge.
Morison, ruled out of Leeds' clash with leaders Cardiff on Saturday due to a thigh injury, told the club's official website: "I got a phone call to say Norwich had agreed a swap for me and Luciano Becchio, and it didn't take long to make my mind up. I'm pretty happy.
"There were lots of rumours going around, but I've been out injured and was concentrating on getting fit. This has all happened quickly in the end, but when Leeds come in for you and you see the place it's a no-brainer."
Morison, for whom Norwich paid Millwall £2.8million in the summer of 2011, struck nine goals for the Canaries in the top flight last season.
He added: "I don't think Leeds are a million miles away from the Premier League and the club is geared up for it.
"The goal is to get to the Premier League and I wouldn't have gone to a club that I didn't think could fulfil that.
"Of course there's pressure on, and the gaffer wants to win promotion, but I think I'm very grounded and I want to be back playing in the Premier League."