The 41-year-old was hospitalised earlier this month after experiencing chest pains and although he was since discharged, he has decided to step down.
"I was closely involved with the appointment of Billy McKinlay, because I was aware that I may not be able to return," he told the club's website.
"I always wanted an experienced British coach within our set-up, because it's important to have that mix of cultures and experience with this squad."
Scott Duxbury, the club's chief executive, added: "We appreciate Oscar's candour in placing the best interest of Watford FC ahead of his own personal thoughts and we wish him well for his future in football."
McKinlay, 45, is a former Scotland international and currently assistant manager of Northern Ireland.
(Reporting by Martyn Herman; Editing by John O'Brien)
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