Janet Commins' body was found near a school field in Flint, north Wales, by three children playing hide and seek.
Stephen Hough, 58, from Flint, was convicted of manslaughter, rape and sexual assault at Mold Crown Court last week. He was cleared of murder.
Hough was sentenced to 12 years and a further three after admitting sexually assaulting a 15-year-old girl in 2016.
The two sentences will run consecutively.
After his arrest following the 2016 incident, Hough's DNA matched samples found on Janet's body, prompting his arrest and subsequent trial on charges relating to her death.
Talking about the offences dating back to 1976, Mr Justice Lewis said Hough had shown "no remorse whatsoever for what you did to that young girl".
"You knew what you were doing... for your own sexual pleasure".
Hough was jailed for 12 years for manslaughter, eight years for rape and eight years for sexual assault - the sentences will run concurrently.
The judge said he took into account the fact Hough was 16 when he committed the crimes.
Janet went missing after leaving her home to go swimming on 7 January 1976.
Four days later, her body was found under a thicket near a school playing field. She had been suffocated during a sexual assault.
Noel Jones, who was 18 at the time, admitted killing her and served half of a 12-year prison sentence.
Although he has never challenged his conviction, he told Hough's trial he was made a scapegoat by police because he was a barely literate Gypsy.
Hough was questioned after Janet's death but was ruled out by police after he said he was stealing petrol the night she was killed - an offence for which he was fined.
In 2016, his DNA was taken by police in an unrelated matter and a match was found with samples taken from Janet's body at the time.
The jury heard it was a billion times more likely to belong to Hough than anyone else.
Senior investigating officer Det Supt Iestyn Davies said: "Very quickly after his DNA was taken [in 2016] and entered on the database, it hit against a crime stain from that 1976 investigation and that prompted us to fully reopen the case."
Trisha Foley, scientific support officer with North Wales Police, praised the "foresight" of the scientists dealing with the case at the time.
"The fact that the material was placed onto slides and then a slip was added over actually preserved that evidence.
"To obtain not only a profile but a full DNA profile with a statistical probability of one to a billion that it matched Stephen Hough, in that timescale - that's a significant result."
The court heard Hough had been court-martialled in 1988 for grievous bodily harm with intent while serving as a soldier in Germany.
He attacked a hotel receptionist and was in the process of "strangling" her when he was disturbed by others.
He was jailed for five years, reduced through the ranks and discharged.
Det Supt Davies added: "Janet was subjected to an horrific, sustained and brutal sexually-motivated assault and the impact upon her family, friends an the entire community was enormous.
"Hough is now in prison, where he rightly belongs."
In a victim impact statement read out in court, Janet's uncle Derek Ireston described his niece as a "loving child, slightly timid and shy, but fun to be with".
He said Hough "stole Janet's future" and her mother Eileen has been "hurting and suffering for 41 years".
His statement added: "The investigation in 1976 seemed to me to be shoddy... anything as a family that we put forward was dismissed.
"We also, as a family, feel for Noel Jones who has also suffered so much since 1976."
The Independent Police Complaints Commission is investigating how North Wales Police handled the original investigation.
Iwan Jenkins, of the Crown Prosecution Service, said: "The huge advancements in forensic testing since the 1970s were the key factor in being able to bring this case to court.
"Our thoughts have been with Janet's family throughout the investigation and trial. They now have the assurance of knowing that her killer has finally been brought to justice."
A man who raped and killed a 15-year-old schoolgirl in 1976 has been jailed for 15 years.