Mr Bailey's solicitor, Frank Buttimer, said the case was withdrawn following discussions with the Du Plantier family's Dublin-based solicitor, Robert Dore. A notice of discontinuance in the case was lodged earlier this week.
Mr Buttimer also confirmed that, in a reciprocal gesture, Mr Bailey is to forego any entitlement to legal costs.
He said the decision by the Du Plantier family to drop their civil case was a "significant development". He said Ms Du Plantier's family her parents Georges and Margaret Bouniol along with Sophie's son Pierre Louis Baudey had decided against continuing with the action following legal advice.
Sophie's husband Daniel Toscan Du Plantier, who died in 2004, was also a plaintiff in the case.
Mr Dore said the family was now reliant on the garda investigation and were unlikely to pursue any other legal avenues.
"As a family, they are appalled that the murderer of their daughter has not been apprehended," he added.
Mr Bailey, a former freelance journalist and landscape gardner, was arrested twice in connection with the death of Ms Du Plantier but has maintained his innocence. Her battered body was found on a laneway close to her holiday home near Toormore, in West Cork, on December 23, 1996.
Mr Buttimer claimed the Du Plantier family had been "led up the garden path" by the gardaí regarding the case and, as such, were victims of the same process affecting his client.
He suggested the Du Plantiers were now "expressly or tacitly" accepting that Mr Bailey had played no part in the death of Ms Du Plantier.
Last October, Schull shopkeeper and key witness Marie Farrell withdrew statements made to gardaí which had placed Mr Bailey close to the murder scene in December 1996. She also made a number of complaints against gardaí, claiming she was intimidated.
Following that Sophie's brother, Bertrand Bouniol, claimed the civil action was "not important" and that it was primarily to provide the family with information into the case.
A garda inquiry into the handling of the original investigation is continuing and Mr Buttimer said he expected it would be completed within the next three months.
"I expect a positive finding that there was garda misbehaviour of a significant nature and if he receives the report I expect he will receive, I expect the commissioner will recommend there should be a full public inquiry into this affair," he said.