Meanwhile, ex-News International chief executive Rebekah Brooks was released on bail after being held for 12 hours over allegations of phone hacking.
"I have taken this decision as a consequence of the ongoing speculation and accusations relating to the Met`s links with News International at a senior level and in particular in relation to Mr Neil Wallis," Paul said in a statement.
"Let me state clearly, I and the people who know me, know that my integrity is completely intact," BBC quoted him as saying.
"I may wish we had done some things differently, but I will not lose sleep over my personal integrity."
Paul stepped down amid growing anger at the failure by Scotland Yard to reveal it had paid Wallis at a time when his force was being criticised for its failure to re-open its investigation into alleged criminality at the now defunct Sunday newspaper.
In standing down, Paul said he had no knowledge of the extent of the phone hacking.
Home Secretary Theresa May said she was "sorry" he had resigned and thanked him for all the work he had done during his time in office.
She said: "Sir Paul has led the force through difficult times and although current circumstances show that there are still serious issues to be addressed, I believe that the force is operationally stronger today now than it was when he took over."
Downing Street sources have denied that Paul was forced to resign, BBC reported.
"He was not pushed," said a source.
The sources also rejected suggestions Prime Minister David Cameron was furious at Sir Paul`s failure to inform him of his connections with former News of the World deputy editor Neil Wallis.
"The PM was not in some rage. He was not furious. He was slightly surprised," a source added.