The Public Prosecution Service said there was enough evidence to prosecute Soldier F for the murders of James Wray and William McKinney.
The 13 demonstrators were killed participating in a civil rights march in the majority Catholic area of Bogside when soldiers from the British Parachute Regiment opened fire on January 30, 1972. The veteran, identified as Soldier F, will also face prosecution for the attempted murder of four others.
But 'in respect of the other 18 suspects, including 16 former soldiers and two alleged Official IRA members, it has been concluded that the available evidence is insufficient to provide a reasonable prospect of conviction, a prosecutor's statement said.
The families of the victims of Bloody Sunday have hoped for years to have those who fired the fatal shots held accountable for the deaths.
Families of the victims will be told if any of the former soldiers, now in their 60s and 70s, are to face charges shortly before the news is made public.
Relatives march from the Bogside to the Guildhall in Londonderry, Northern Ireland.
Former soldiers who killed thirteen men on Bloody Sunday will learn today if they're to be charged with murder.
The decision to prosecute one former soldier who was serving in Londonderry on Bloody Sunday is "one too many", a veterans' group has said. But the PPS has announced it will begin considering perjury charges against them.
John Kelly, whose 17-year-old brother Michael was shot dead, said: "The dead can not cry out for justice, it is the duty of the living to do so for them".
He went on to promise full backing to Soldier F, including the provision of unlimited cover for his legal costs, and praised British Army members who "served with courage and distinction to bring peace to Northern Ireland".
James Wray's brother Liam said he was "very saddened for the other families" of those killed on Bloody Sunday.
"Today is a stark reminder that victims have always been paying the price for the failure of government to effectively deal with the past".
The investigation into prosecuting the former soldiers for actions decades ago at a time of increased tensions in Northern Irelands has been controversial.
"If it is in the public interest to suspend prosecutions and release terrorists early from prison, it can not be in the public interest after almost half a century to prosecute these people", Richard Benyon, a ruling party MP and former British army officer, told The Times.
Police launched the murder investigation after a 12-year inquiry report published in 2010 criticised soldiers and refuted claims that some of the marchers had been armed and attacked troops. "Do not deny us justice any longer".
The inquiry was authorised by then-Prime Minister Tony Blair in 1998 ahead of the negotiations that led to the Good Friday peace accord.
However, much of the material collected by the Saville investigation in which former paratroopers were given anonymity and broad protections from criminal charges, was inadmissible, prosecutors said, in criminal proceedings "due to strict rules of evidence".
They took further heart from then prime minister David Cameron's apology.