The 16-year-old was reportedly courted by Spurs and Arsenal too.
The Hammers, who signed Toni Martinez from Valencia on Friday, are understood to have won a competitive race to sign 16-year-old Quina.
The Portuguse ace, predominantly an attacking midfielder, had been at Chelsea but is believed to favour a switch to the Irons in the belief that his first-team chances would be strongest there.
Should they sign Quina - also a Portugal Under-17 international - it would speak volumes for the respect that Slaven Bilic is beginning to command with regards to young players.
Gunners boss Arsene Wenger had often been the go-to-guy for nurturing young talent, but it would appear as if East London is now the place to be for starlets.
Bilic has also tied up deals for highly-rated youngsters Martin Samuelsen and Sam Ford since replacing Sam Allardyce, in addition to the recent acquisition of 18-year-old Martinez.