The 34-year-old had been on trial at the American club and impressed in pre-season.
Piquionne, who made one international appearance for France and has more recently represented Martinique, played over 80 matches in the Barclays Premier League after joining Portsmouth in 2009 and then West Ham a year later.
He fell out of favour at Upton Park after Sam Allardyce took over as manager in 2011 and spent time on loan at Doncaster before leaving the Hammers earlier this year.
Timbers head coach Caleb Porter told the club's website: "Frederic made a strong impression during his trial and gives us another quality piece in the striker position.
"He is a proven professional at a high level and helps our depth with Bright Dike out. We are very pleased about this addition to our club."
Piquionne, who has also played for Rennes, St Etienne, Monaco and Lyon, joins compatriot Mikael Silvestre at the Timbers after the former Manchester United defender, 35, completed his free transfer to the club last week.
Both men are in line to make their debuts in Sunday's MLS season-opener against New York Red Bulls.