Ms Brankin, who was 51, is understood to have died of natural causes at her Birmingham home on Sunday.
Her son, Sapper Quinsey, was murdered by the Real IRA at Massereene Barracks in Antrim in 2009.
The 23-year-old was gunned down along with 21-year-old Sapper Patrick Azimkar, as they went to collect pizzas.
Last year Ms Brankin attended a commemoration in Antrim with her daughter, where a memorial was unveiled to the two soldiers.
Speaking on behalf of Antrim Borough Council, the Mayor, Councillor Roy Thompson said: "It was with great sadness that we received the news of the death of Mark Quinsey's mother, Pamela.
"Over the past four years, Antrim Borough Council has formed a strong bond with both the Quinsey and Azimkar families.
"We know that Pamela has been in very poor health since Mark's murder and now both families, who have become firm friends, have suffered another loss.
"Their suffering continues and our deepest sympathy is with Pamela's family circle, in particular her daughter Jaime who, in her grief, has always shown remarkable courage and dignity."
He continued: "There's no doubt in my mind that Mark's mother, Pamela, is yet another victim of the terrible atrocity that took place at Massereene Barracks on 7 March 2009."
The Mayor said he hopes that the people of the Antrim Borough will be represented at Ms Brankin's funeral.
Ulster Unionist Party leader, Mike Nesbitt MLA expressed sadness on behalf of his party at the passing of Ms Brankin.
"The Ulster Unionist Party is very saddened to hear of the death of Pamela Brankin, the mother of Sapper Mark Quinsey and we send our sympathies to her family and friends," he said.
"She is one of the thousands of untold and unrecognised victims of the violence in Northern Ireland.
"The legacy of the grubby terrorist campaign is endless human suffering.
"As a Victims Commissioner, I learnt to be mindful that beyond those who lost their lives as a direct result of terrorist attacks, many others died of broken hearts, heart attacks and many many more suffer mental health issues that will be with them to the grave."
Co Londonderry man Brian Shivers is currently on trial accused of killing the two soldiers.
On Thursday the prosecution are due to make their closing arguments in the case.