Thomas is signing a two-year deal, according to sources with knowledge of the deal.
"We're excited to be adding the experience, toughness and veteran leadership that Kurt will provide for our team," acting general manager Chad Buchanan said in a statement. "We've long respected Kurt and expect him to make a strong contribution to our organization."
Thomas, 39, is the league's oldest active player and will join fellow Dallas native LaMarcus Aldridge in the Blazers' frontcourt rotation.
Thomas spent last season in Chicago. Portland will be the ninth team for Thomas, who has averaged 8.6 points and 6.9 rebounds in 16 seasons.
Marc Stein is a senior NBA writer for ESPN.com.