The 26-year-old has signed a three-year deal at The Hawthorns and joins Shelton Martis and Craig Beattie as new signings this summer.
Mowbray said: "Filipe is a creative midfielder from Portugal.
"He's a talented, very technical player who we identified and we're delighted he's joined us.
"He will hopefully play a big part in what we are trying to achieve."
Teixeira started his career at Felgueiras before moving to French Ligue One club Istres in 2001.
He then enjoyed a spell alongside Ronaldinho at Paris Saint-Germain before moving to Coimbra in 2005.