The teenager joins the Vicarage Road residents on a four-year contract, with the club retaining the right to extend the deal by adding a further year.
Quina, who had stints at both the Benfica and Chelsea youth academies, joined West Ham two years ago.
He made two appearances for the Londoners during their 2016/17 Europa League campaign and is regarded as one of Portugal's brightest young prospects, having starred for his country at youth level.
"The Hornets are delighted to announce the deadline day signing of highly-rated Portuguese attacking midfielder Domingos Quina," the Hornets announced via their club website.
"Quina, an exciting 18-year-old who has attracted the attention of some of Europe’s biggest clubs this summer, has agreed a four-year contract and moves to Vicarage Road from West Ham.
"Watford also hold the option on an additional 12 months for the talented Portugal Under-20 international."
Watford did not mention a fee but it is believed that the deal cost them around £1m plus potential add-ons based on performances.