Fourteen civilians were killed when British soldiers fired on a crowd after a civil rights march in the city.
The veteran will face prosecution for the murders of James Wray and William McKinney and the attempted murders of Joseph Friel, Michael Quinn, Joe Mahon and Patrick O'Donnell.
The UK's Defence Secretary said the individual affected by the ruling will be offered full legal support. Thirteen people were killed, 14 were wounded and one of the wounded later died.
Soldiers take cover behind their sandbagged and armoured cars while dispersing rioters with CS gas during the Bloody Sunday riots.
However the available evidence surrounding 18 other suspects - 16 paratroopers and two alleged Official IRA members - who were investigated for charges up to and including murder was insufficient to provide a reasonable prospect of conviction, prosecutors decided.
Following the publication of the Saville report in 2010, then prime minister David Cameron apologised for the Army's actions, branding them "unjustified and unjustifiable".
Families of the victims said they were "disappointed" by the decision to press charges against just one ex-soldier, and revealed they may ultimately bring a challenge to the High Court after giving a "detailed consideration" to the reasons provided by the PPS.
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He said: "We are indebted to those soldiers who served with courage and distinction to bring peace to Northern Ireland. Our serving and former personnel can not live in constant fear of prosecution".
Police in the North opened their investigation into the killings after the 2010 Saville Report found that British troops opened fire on Bloody Sunday without issuing a warning.
He noted that today "will be another extremely hard day" for family members of the victims of the massacre and noted that he met with them personally "to explain the prosecution decisions taken and to help them understand the reasons".
However, the government has proposed legislation to widen the programme to offences taking place from 1968, meaning any Bloody Sunday prosecutions would be eligible.
But the PPS decisions in respect of potential perjury charges will be announced at a later date. "In these circumstances the evidential test for prosecution is not met".
The marchers had been protesting Britain's detention of suspected Irish nationalists in the majority Catholic area of the Bogside in Derry on what became known as "Bloody Sunday", January 30, 1972.
He added: "I am mindful that it has been a long road for the families to reach this point and today will be another extremely hard day for many of them".