Oden and 2007 draft picks Petteri Koponen, Taurean Green and Josh McRoberts all came to terms with the Trail Blazers, the team said on its Web site.
Terms of the deals weren't released but under the NBA's collective bargaining agreement, Oden's contract will be for two years with Portland having options on a third and four year.
"When I signed my contract I felt like an official NBA player," Oden said on the Web site announcement. "They showed me everything and the amount looked pretty good."
Oden, a 7-foot center, played one season for Ohio State, leading the Buckeyes to the NCAA championship game. He averaged 15.7 points, 9.6 rebounds and 3.3 blocked shots over 32 games.
All of Portland's recent signees are expected to participate on the team's summer league team, which begins play Friday.