They are hoping that the 50-year-old will released today from Maghaberry prison.
It is understood the Parole Commissioners directed his release after 993 days of incarceration.
However, it is not clear if any conditions will be attached to his release, which could included no commenting in public about his case. ]
A similar condition was imposed on another republican prisoner, Martin Corey, when he was set free from jail several in 2014. As well as a ban on talking to the media, he was exiled from his Lurgan home to Dungannon for six months before he was allowed home.
Tony has been held behind bars since March 2016 after his early release licence was revoked by then British Secretary of State Theresa Villiers.
She ordered him to be thrown back in jail on the word of MI5.
A campaign was later launched to highlight his case with supporters claiming he was the victim of internment.
His wife Lorraine, who has been spearheading the campaign for her husband’s release, said her family will be “thrilled” to have him home.
“It will really make our Christmas special for us,” she said.
“Myself, the children and Tony’s parents are all delighted and very relieved to have him back with us.”
Ms Taylor said her family still has concerns.
“We are concerned nonetheless at some of the punitive restrictions which continue to be placed on Tony, who has already spent the equivalent of a five-year sentence in jail without charge,” she said.Mr Taylor’s parents are both ill and housebound, while his son Blaine has a profound disability.
Earlier this month Mr Taylor’s father Willie wrote to Secretary of State Karen Bradley appealing for his son’s release.
The father-of three was seriously injured in a premature bomb explosion in Derry in 1994.
In a follow up search police found a Mark 16 mortar.
He was sentenced to 18 years in prison and released under the Good Friday Agreement.
In 2011 he was sentenced to seven years for possession of a rifle, with three years to be served in custody and four on licence.
Sinn Féin MLA Raymond McCartney also welcomed the Derry man’s release.
“News of Tony Taylor’s release today is welcome but doesn’t change the fact that he should never have been returned to prison in the first place,” he said.
“His release comes after 993 days wrongful detention, during which time the British government consistently failed to produce any evidence which could in any way justify his incarceration.”
Independent Derry City and Strabane councillor Paul Gallagher said “the council’s corporate position was to support his release”.
“I’m glad he was released but we have to look to ensure there are no more Tony Taylors,” he said.
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