The settlement announced at the High Court on Friday covers financial loss over the death of married father-of-six Paddy Doherty in Derry in January 1972.
A further claim against the Ministry of Defence for aggravated damages remains unresolved.
Mr Doherty, 31, was among 13 people killed when members of the Parachute Regiment opened fire on unarmed civilians in the city.
He was shot from behind while prone on the ground close to the Rossville Flats.
In 2010, the Saville Inquiry into the events on Bloody Sunday established the innocence of all those killed and wounded.
Those findings led to the British Prime Minister at the time, David Cameron, issuing a public apology for the soldiers’ actions.
He described the Bloody Sunday shootings as “unjustified and unjustifiable”.
More than £2 million has already been paid out in settlements and awards made in other actions against the MoD on behalf of those bereaved or injured.
With liability accepted in all cases, proceedings brought by Mr Doherty’s relatives centred on the level of damages.
In court today, Brian Fee QC, for the family, told Mr Justice McAlinden: “We have agreed the financial loss aspect, the figure is £307,324.”
The aggravated damages claim was adjourned pending the outcome of an MoD appeal against an earlier award of £15,000 for injury to the feelings of another man who died on Bloody Sunday: 41-year-old Bernard “Barney” McGuigan.
According to the Saville Inquiry report Mr Doherty had been in a crawling posture when shot by Lance Corporal F.
Four of the dead man’s children were present for the settlement in the action.
Outside court the family’s solicitor, Fearghal Shiels of Madden & Finucane, said they were relieved this part of their case was now over.
But he stressed: “The circumstances of their father’s death should not be forgotten.
“Paddy Doherty was shot from behind, attempting to crawl to safety from army gunfire when, as the Saville Inquiry concluded, he was shot without justification by Soldier F.
“Today represents a total vindication of his innocence.”