Carrick, who will have a testimonial at Old Trafford this summer, completed his move from Spurs in 2006 for a fee of £18million.
He has gone on to make nearly 450 appearances for United, proving one of their most valuable signings of the Premier League era.
But Ferguson says that United were made to work to secure the signing, as Levy, who is notoriously tough in transfer negotiations, ensuring Spurs got the right end of the deal.
“I must say negotiations were very difficult and went on for ages,” legendary United boss Ferguson told MUTV .
“I always remember I thought it was done and [former chief executive] David Gill phoned me on the golf course to say they want more. Typical [Spurs chairman] Daniel Levy!
“It was very hard to negotiate but, at the end of the day, we got it through and, ever since he joined us, he’s had a fantastic career.”
A Geordie by birth, Carrick was snapped up by West Ham at the age of 16 and went on to play with the Hammers until 2004, before his move to Spurs.
He spent two years at White Hart Lane before Ferguson picked him up – and the 75-year-old said that he knew straight away that he was going to be a big signing.
Stormzy gets star-struck meeting Michael Carrick
“From the minute we bought him, his character has always been absolutely outstanding,” Ferguson said.
“He’s a football man and that character, plus his ability, made him a certainty to be a big success here.
“When we were discussing him and were ready to make a bid, we were looking at his background and one of the things that stuck out to me was as a young boy, he went down to play for West Ham.
“A 16-year-old kid going way down from Newcastle to east London – that’s a trek, and it epitomised to me the confidence the boy had in himself. That impressed me.”