The entertainer was speaking after being told by police he would face no further action in the UK after he was arrested on suspicion of historic sexual offences. One remaining claim has been referred to an authority outside the UK.
The 59-year-old was held in January by detectives from Operation Yewtree, the national investigation sparked by the Jimmy Savile abuse scandal, and re-arrested in March after further allegations emerged. His arrest was not linked to the late DJ.
Davidson said: "I'm just pleased there will be no further action."
He added: "I kept on working because I was innocent and that is what I believed from the beginning."