The 29-year-old winger joins the Baggies on loan from Porto, having won the Europa League in 2011, and becomes the club's 10th signing of a busy summer transfer window
The Portugal international becomes the 10th new arrival at the Hawthorns since the end of last season after passing a medical.
The versatile wideman has 26 international caps to his name and arrives in the Premier League with a record of 30 goals from 115 Primeira Liga appearances for Porto.
"Silvestre is a vastly-experienced player, both with Porto and his national team, and I'm delighted we've managed to secure his services," said head coach Alan Irvine.
"He's got pace and power, gets his fair share of goals and is also a creator of chances for others.
"He's a fantastic addition to our squad."
The 29-year-old was part of the Porto team that won the Europa League in 2011.
He joins a West Brom side who have started the Premier League season with draws against both Sunderland and Southampton.