A source at the Department of Justice has confirmed that Co Donegal man Gallagher is now being detained.
Gallagher, who killed mother and daughter Anne and Annie Gillespie in the grounds of Sligo Hospital in 1988, was living in Strabane, Co Tyrone.
Gallagher, from Lifford, killed Anne, 22 and her mother Annie, 51, after learning how Anne planned to dump him.
Gallagher also tried to kill Anne’s uncle Patrick Maguire but the gun jammed when he tried to shoot him.
Gallagher, who was then 22, was tried for murder but was found to be insane.
Twelve years later he escaped from Dundrum Central Mental Hospital and fled to England where he lived for a number of years.
However he returned in 2003 and set up home in Strabane just a few miles from where his victims lived in the Twin Towns of Ballybofey and Stranorlar.
Gardai have constantly said they could not arrest Gallagher unless he crossed the border into the Republic.
He was not wanted in Britain because he committed no crime there.
Gardai in Donegal had not been made aware that Gallagher had handed himself in.
There has been a stunned reaction to the news that Gallagher has handed himself in.
There is a split in the Gallagher family which means that the double killer has not spoken to some of his family for many years.
He is still on speaking terms with brother Christopher and his mother who still live in Lifford.
However he is estranged from the rest of his family.
One of those close family members, who asked not to be named, said John Gallagher was “not mad but bad.”
“He knows exactly what he is doing by handing himself in. He will be trying to get out as soon as he can.
“He was never insane. How come all of a sudden he thinks he is well enough again and hands himself into a mental hospital.
“He has been living in Strabane for the past ten years almost and he had plenty of time to hand himself in but chose not to.
“He is playing everyone for fools but people have to see through this,” said the family member.
Gardai have played down as “wild rumours” claims that Gallagher handed himself in to officers here in Donegal.
Gallagher went to Dundrum on his own on Tuesday.