The 34-year-old former France international impressed during a trial with the Major League Soccer side.
He made 40 appearances for the Hammers, scoring 11 goals, and spent part of last season on loan at Doncaster Rovers.
Piquionne will join up with former Manchester United and Arsenal defender Mikael Silvestre in Portland.
He said: "I am delighted to sign for Portland. It is a one-year contract. Mikael Silvestre is here with me, so settling in will not be as difficult as I think.
"We will try to do very well, as much as we can for Portland. For me, it will be another great experience to play in another great league."
Piquionne, who earned one cap for France, also played for Portsmouth during his time in England. He signed for West Ham from Lyon for £1million in July 2010.