The Blazers are retaining Thybulle, 26, who will stay a part of the franchise's rebuild as the organization also pursues trades of franchise star Damian Lillard.
The deal includes an $11.5 million player option in the third year, sources said.
Thybulle signed the offer sheet Thursday and Portland officials made a decision within an hour to match the sheet and retain him, sources said.
Thybulle is one of the Blazers' best defenders and fits with the team's young core. Portland acquired him in February from the Philadelphia 76ers. He played his first four-plus seasons with the 76ers before landing with the Blazers at the February trade deadline. He started 22 games in the final weeks of the season, averaging 7.4 points and 1.7 steals in 27 minutes.