The 39-year-old Thomas played 52 games with the Bulls last season and averaged 4.1 points and 5.8 rebounds per game.
"We're excited to be adding the experience, toughness and veteran leadership that Kurt will provide for our team," said Blazers acting general manager Chad Buchanan. "We've long respected Kurt and expect him to make a strong contribution to our organization."
Portland will be the ninth spot on Thomas' vagabond career, as he's played for Miami, Dallas, New York, Phoenix, Seattle, San Antonio, Milwaukee and Chicago.
He owns career averages of 8.6 points and 6.9 rebounds over 16 seasons.