Ms Drumm will be played by Fleetwood, a Tony Award-nominated English screen and stage actress whose recent credits include a role in the award-winning film Philomena.
She also played minor roles in the film adaptations of Les Miserables and Harry Potter and the Deathly Hallows: Part 1.
Webster's first wife, Ms Morris, will be played by acclaimed English actress Sheridan Smith, who won a Bafta for her role in the five-part series Mrs Biggs.
Fiancee and intended third victim Simone Banarjee, who testified against Webster at trial, will be played by Archie Panjabi, who stars in television series The Fall.
The Herald previously reported that Webster would be played by League of Gentleman star Reece Shearsmith.
Ms Drumm's sister last year said the family did not want to comment on the series, but Ms Morris' brother said he supported the production as it was being made respectfully.
The series is co-written and produced by award-winning ITV screenwriter Jeff Pope, who was quoted in British media as saying the story was "far more chilling than any fiction''.
"Webster was a banal, almost benign face of evil. He was so clever at hiding his tracks and presenting a plausible front to his friends, family and colleagues that he was able to do what he did without really attracting suspicion.
"The courage and tenacity of Webster's second wife Felicity, and his last intended victim Simone, is all that stood between him and potentially more murders.''
Webster and Ms Drumm met while working as nurses in the Middle East and married in Auckland following a whirlwind romance in 1997.
He started plotting almost immediately, drugging Ms Drumm on their honeymoon before staging a serious car crash on Auckland's Northwestern Motorway in 1999.
After the crash, Drumm's family discovered he had withdrawn all the money from their joint bank account and forged life insurance policies for his wife.
Ms Drumm reported his actions to Scottish authorities, and Webster was found guilty in 2011 and sentenced in the High Court at Edinburgh to a minimum non-parole period of 30 years