The 52-year-old is on trial for the second time accused of sexually assaulting and strangling Karen Hadaway and Nicola Fellows in 1986.
The girls, from Brighton, went missing and were found dead in a woodland den in Wild Park on the South Downs a day later.
In 1987, Bishop was cleared of their murders but was ordered by the Court of Appeal to stand trial again in light of new evidence following advances in DNA testing.
He denies two charges of murder.
Jurors at the Old Bailey were told examination of a light blue paint-stained Pinto sweatshirt, which the prosecution said was discarded by Bishop as he walked home, had revealed “compelling” evidence.
Brian Altman QC, prosecuting, said there was “wealth of evidence to show this man, Russell Bishop, to the exclusion of anyone else in the world, is guilty of the murder of those two little girls 32 years ago”.
He added: “There is powerful evidence of a physical connection between him and those girls; the person who wore the discarded Pinto sweatshirt was the killer and it was the defendant who wore it.”
He said the evidence included the transfer of fibres, paint comparisons and DNA.
“We say you can conclude that the Pinto sweatshirt obviously belonged to him, that it came into recent contact with the girls’ clothing and that recent contact can only have been at the time of their murder,” said Mr Altman.
The court heard how more evidence came from a taping from Karen’s left forearm, which had not previously been examined.
Jurors were told it provided a one-in-a-billion DNA match to Bishop.
Mr Altman also examined the similarities between the murders and the crime Bishop was convicted of – the kidnap, sex assault and attempted murder of a seven-year-old girl from Brighton three years later.
The prosecutor said circumstantial evidence also pointed the “finger of guilt firmly in this man’s direction”.
It is claimed Bishop was seen in Wild Park at the time and later described details about the murder scene, which the killer could only have known.
Mr Altman told jurors about contradictions and admitted lies in Bishop’s accounts.
“It is, say the prosecution, the overwhelmingly compelling and powerful nature of all the evidence in this case that can make you sure of this defendant’s guilt of these murders,” said the prosecutor.
The trial continues.