He was unveiled at a press conference on Friday afternoon where Woodgate was asked if he was pleased to be joining Newcastle and answered: "I’m thrilled to be fair, I’ve been at Leeds since I was 13 years old and I’m sorry to be leaving my friends behind.
"I don’t feel like I’ve been pushed out, Newcastle made a bid for me that was accepted and I chose to come here.
"Peter Ridsdale has taken a lot of unfair stick about my move, but he’s an honourable man and stuck by me through thick and thin, through the court case and everything.
"But I’ve learnt my lessons from the court case, I’ve come through it and I think I’m a better player.
"Now I’ve got a big chance to win the Premiership this year, next year and for the next few years. We’ve got a great young squad and hopefully we will win trophies.
"There was no one reason I chose to come here, there are great players, a great manager and 50,000 supporters every week. I’ve known Kieron Dyer and Andy Griffin for a couple of years, as well as Gary Speed and Alan Shearer, so hopefully I’ll settle in well."
Asked about objections raised about his past Woodgate added: "I’m not a racist, ask Michael Chopra, Harpal Singh or Kieron Dyer.
"I’m not a racist, I’m Black and White."
Sir Bobby was also delighted with the signing, saying: "This is the biggest financial signing in Europe, not just in England, in Europe.
"We’re close to the big boys, Arsenal and Manchester United and this signing shows our ambition.
"I’ve wanted a top class defender for a while and felt it was prudent to buy English.
"We’ve a lot of foreign players at the club who are good pros but the balance has to be right. He’s a Northern boy and won’t need time to settle in.
"I’m confident he will be a great player for Newcastle United, there is no risk attached to signing Jonathan."
Earlier Freddy Shepherd told the club’s official website: "He is a great young player and another player we have signed for the future so we’re delighted.
"Once again we have proved our ambition as a club by backing the manager in the transfer market.
"I hope he will be with us for the rest of his career. It was perfect timing for Newcastle with the window about to close on Friday evening, but I was always confident we would get him in time.
"Another bonus is that he is from the North East, so he knows all about the passion for football in this area and he knows all about the way of life – as well as the freezing cold weather up here!"