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The comedian, who has always denied any allegations against him is “pleased” with the decision his solicitor says.
Mr Davidson was arrested in January as part of Operation Yewtree, the investigation sparked by the Jimmy Savile abuse scandal, although there was no connection to Savile himself.
The claims against him were said to involve a number of women and date back as far as 35 years.
Mr Davidson was told, along with a 53-year-old man also arrested in January, that they will face no further action when they answered police bail on Wednesday.
Prosecutors said that there was insufficient evidence in relation to 10 allegations, one of which related to both men, and nine others that were made against Davidson.
Prosecutors have offered to meet with any of the complainants to discuss the decision to take no further action.