4 April 2011 Last updated at 12:36 GMT
The body of Ms Halstead, 33, was found in a Rotterdam canal in 1990.
The body of Ms Fields, 31, was found in London's Regent's Canal in 2001.
The cases were linked in February 2010.
Sweeney was also found guilty of perverting the course of justice.
The murderer could be sentenced in the afternoon, Mr Justice Saunders said.
Officers are trying to trace Sweeney's other former girlfriends as they believe he may have killed other women.
Detectives are currently trying to trace two South American former girlfriends, who have not been seen since the late 1990s.
One was a Brazilian woman known as Leani, the other a Colombian called Maria.
The killer was described in court as a "hateful, controlling and possessive man".
The dismembered and headless body of Ms Fields was found in body bags in London's Regent's Canal in 2001.
The torso of Miss Halstead was found in a canal in Rotterdam, Holland, in 1990, the court heard.
Gruesome artworks Sweeney, who lived in Hackney and Camden in London, also tried to kill a third girlfriend, Delia Balmer.
He was given four life sentences for the axe attack on Miss Balmer in 1994, the court heard.
During the trial the court heard that the carpenter had cut off the heads and hands of Miss Halstead, a US citizen, and Miss Fields, which was a deliberate attempt to prevent the victims from being identified. The body parts have never been found.
Detectives found several weapons and 300 pieces of gruesome artwork and poems in his north London house. Several other such artworks were found in his prison cell.
A man has been found guilty of murdering two of his former girlfriends and throwing their bodies in canals in London and the Netherlands.
John Sweeney, 54, of no fixed address, denied the murders of Paula Fields and Melissa Halstead and perverting the course of justice, at the Old Bailey.The body of Ms Halstead, 33, was found in a Rotterdam canal in 1990.
The body of Ms Fields, 31, was found in London's Regent's Canal in 2001.
The cases were linked in February 2010.
Sweeney was also found guilty of perverting the course of justice.
The murderer could be sentenced in the afternoon, Mr Justice Saunders said.
Officers are trying to trace Sweeney's other former girlfriends as they believe he may have killed other women.
Detectives are currently trying to trace two South American former girlfriends, who have not been seen since the late 1990s.
One was a Brazilian woman known as Leani, the other a Colombian called Maria.
The killer was described in court as a "hateful, controlling and possessive man".
The dismembered and headless body of Ms Fields was found in body bags in London's Regent's Canal in 2001.
The torso of Miss Halstead was found in a canal in Rotterdam, Holland, in 1990, the court heard.
Gruesome artworks Sweeney, who lived in Hackney and Camden in London, also tried to kill a third girlfriend, Delia Balmer.
He was given four life sentences for the axe attack on Miss Balmer in 1994, the court heard.
During the trial the court heard that the carpenter had cut off the heads and hands of Miss Halstead, a US citizen, and Miss Fields, which was a deliberate attempt to prevent the victims from being identified. The body parts have never been found.
Detectives found several weapons and 300 pieces of gruesome artwork and poems in his north London house. Several other such artworks were found in his prison cell.
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