Arthur Smyth, a former resident of the Kincora home, has waived his anonymity to make the allegations against the earl, a great uncle of the King.
Lord Mountbatten was killed along with three others when the IRA detonated a bomb on his boat in Mullaghmore, Co Sligo, in 1979.
Mr Smyth’s solicitor, Kevin Winters of KRW Law, said the civil action alleging negligence and breach of duty of care was being taken against several state bodies.
He said he had filed a summons which would be issued in the High Court in Belfast on Tuesday.
Mr Winters said: “Central to the case are our client’s allegations of abuse by the late Lord Louis Mountbatten.
“Understandably many abuse survivors for reasons of obvious sensitivity choose to remain anonymous. Arthur’s decision to reveal his identity must be set against this backdrop.
“It is borne out of anger at systemic state cover-up on abuse at these institutions.
“He alleges to have been abused twice as an 11-year-old by the deceased royal.
“It’s the first time that someone has stepped forward to take allegations against Lord Mountbatten into a court.
“That decision hasn’t been taken lightly.
“He understands only too well that it will be a deeply unpopular case with many people coming as it does within weeks of the passing of the Queen.”
The Kincora home opened on Belfast’s Upper Newtownards Road, close to Stormont’s Parliament Buildings, in May 1958, and closed in October 1980 after a sex abuse scandal.
The Historical Institutional Abuse Inquiry found that 39 boys were abused at Kincora and in 1981 three men were jailed for abusing 11 boys.
However, it found no evidence that security agencies were complicit in the abuse.
A recent report by the Police Ombudsman for Northern Ireland (Poni) Marie Anderson said that complaints from some former residents’ about the failure of police to investigate allegations of sexual abuse at Kincora were “legitimate and justified”.
Mr Winters said: “The recent Poni report into Kincora, despite a welcome finding on police investigative failures, only scratches the surface of what really went on.”
These allegations come two years after biographer Andrew Lownie published a book about Lord Mountbatten and his wife Edwina. In his book, he alleged that Mountbatten was not only bisexual but had a weakness for underage men.
On Smyth's allegation, Lownie said: “I am delighted that Arthur Smyth has gone public,”
“It further backs up the claims of the two victims I interviewed who were abused in 1977 and confirms that the claims of paedophilia against Mountbatten in the FBI files can be taken seriously.”