Mr Adams presented himself voluntarily to the station on Wednesday night where he was then arrested and questioned under caution by detectives from the PSNI's Serious Crime Branch.
It is understood Mr Adams presented himself to police just after 8pm.
UTV understands he is being questioned under the Terrorism Act 2000 and can be held for 48 hours before police need to apply to the courts for additional time to continue their interview.
Mrs McConville, a 37-year-old widow and mother of 10 children, was abducted in December 1972 from her flat in the Divis area of the city and shot by the IRA.
She was one of the so-called 'Disappeared' and her body was recovered on a beach in Co Louth in August 2003.
On Thursday morning, the family of Mrs McConville said they were "happy" to see the police investigation moving forward.
Jean's son, Michael, was 11 at the time of the abduction, he told UTV: "All of us - my brothers and sisters - were separated by welfare services. I was put in a home by myself.
"I saw my younger sister maybe four or five times until she was 16 and it was the same with my other brothers and sisters, we were kept apart.
"I never saw them growing up," he said.
Our mother was taken away and we knew she was murdered.
He added: "We got our mother's body back, we were able to give her a Christian burial, for me to see someone charged and convicted of this crime would bring closure.
"For the family we just want to see someone brought to court for this.
"Had you asked me five or 10 years ago would this have happened, I would have said no.
"So we are pleased to see the police investigation moving forward."
No one has ever been charged with the murder, however, in recent weeks there have been a series of arrests.
In March veteran republican, 77-year-old Ivor Bell, was charged with aiding and abetting the murder and five other people have been detained and questioned.
The recent police activity followed a decision by a US court compelling a Boston university to hand over to the PSNI recorded interviews with republicans about Mrs McConville's murder.
Boston College interviewed a number of former paramilitaries about the Troubles on the understanding transcripts would not be published until after their deaths - but that undertaking was rendered ineffective when the court last year ordered that tapes that contained claims about the killing be given to PSNI detectives.
Former west Belfast MP, Mr Adams, 65, has always denied IRA membership or any role in Mrs McConville's death and said in March he would be available to meet with detectives if they wished to speak with him.
Sinn Féin deputy leader Mary Lou McDonald said the arrest was "politically motivated" and designed to damage the party and its president ahead of the upcoming elections.
Following his arrest, Sinn Féin released a statement from Louth TD Mr Adams.
He also raised concerns over the timing of the arrest.
"I believe that the killing of Jean McConville and the secret burial of her body was wrong and a grievous injustice to her and her family," he said.
"Well publicised, malicious allegations have been made against me. I reject these.
"While I have never disassociated myself from the IRA and I never will, I am innocent of any part in the abduction, killing or burial of Mrs McConville."