Redknapp had been favourite to take over from Sam Allardyce as manager for Newcastle.
He said: “I’m happy, I’ve got a great relationship with the fans and the owner.
“To walk away having brought them here wouldn’t be right. It was a great offer.
“To be offered the chance to go and manage a fantastic club like Newcastle was a terrific opportunity, but it wouldn’t have been the right thing to do.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.