Until I Kill You is airing on ITV and the four-part drama is based on the harrowing true events retold by Delia Balmer in her memoir titled Living with a Serial Killer.
Delia is Sweeney's only known surviving victim, with the axe murderer having killed Melissa Halstead and Paula Fields, dumping their bodies in canals.
Melissa, 33, was his first victim and he admitted the murder to Delia during one of his angry tirades, recalling how he sat with her body for days before cutting it up and disposing of it in a river.
Then, while he was on the run following a near-fatal attack on Delia, he killed Paula Fields, 31, and her body was found in Regent's Canal in 2001.
The two murders were linked in February 2010 and Liverpool-born Sweeney was arrested at Gartree Prison in Leicestershire, where he was serving life for an axe attack on Delia.
The former carpenter, 67, is still in prison, where he is likely to remain for the rest of his life.
He had refused to leave his prison cell at Belmarsh prison to hear his sentence after he was found guilty of the two murders.
Judge Mr Justice Saunders, sentencing him, had said: "These were terrible, wicked crimes. The heads of the victims having been removed, it is impossible to be certain how they were killed.
"The mutilation of the bodies is a serious aggravating feature of the murders.
"Not only does it reveal the cold-blooded nature of the killer, but it has added greatly to the distress of the families to know that parts of their loved ones have never been recovered."
It was Sweeney's disturbing artwork that eventually gave him away as clues to his visceral hatred of women were found in a collection of more than 300 paintings and poems.
One, entitled the Scalp Hunter, showed a female victim and a bloody axe.
On the back of a scratchcard he had written a poem: "Poor old Melissa, chopped her up in bits, food to feed the fish, Am*dam was the pits."
Until I Kill You continues on ITV on November 4
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