Manuel Pellegrini has been active in the transfer market since moving to the London Stadium, with the Chilean spending close to £90m on seven first-team additions.
The Hammers have now moved to completed another incoming with Silva - who will begin life in East London with the Under-23s - penning a three-year contract.
The 21-year-old told the club's official website: "This is a very important moment for me. This is a new experience for me, out of Portugal. I am very happy to be here at West Ham.
"I am a technical player and I am very fast. I will give West Ham 100% on the pitch every time I play. It's a big dream of mine to play here in England. This is a club with a big history, with very good fans and I'm very excited to be here."
Silva leaves Vitoria having made seven starts and 19 substitute outings in the first team.