The Raiders announced the signing late Thursday night and said Pryor would take the field for his first NFL practice on Friday.
ESPN's Adam Schefter first reported the deal.
The Raiders play their third exhibition game on Sunday against New Orleans and it would be extremely unlikely that Pryor would play. The Raiders then will have three practices before the exhibition finale at Seattle on Sept. 2.
After that game, Pryor will be ineligible to practice with the Raiders until serving a five-game suspension.
When he was allowed to enter Monday's supplemental draft, Pryor was handed a suspension by NFL commissioner Roger Goodell for the same number of games he would have sat out had he returned to Ohio State. Pryor has said he will not appeal the suspension.
Pryor gave up his final season with the Buckeyes after an investigation into the team's memorabilia-for-cash scandal that cost coach Jim Tressel his job.
Pryor is an impressive physical specimen, measuring 6-foot-5 and 232 pounds and being clocked at 4.36 seconds in the 40-yard dash at his pro day last weekend.
Pryor is coming off his best season statistically at Ohio State, throwing for 2,772 yards and 27 touchdowns with 11 interceptions. He ran for 754 yards and four TDs while helping the Buckeyes win the Sugar Bowl.
There has been some speculation that Pryor could eventually play receiver or tight end in the NFL, but Raiders coach Hue Jackson said Monday that Pryor will start off as a quarterback.
The Raiders considered drafting a quarterback to groom for the future in April but did not find the right fit. Now they have Pryor to fill that role.
Oakland is without picks in the second, third and fourth rounds in next year's draft. The Raiders traded the 2012 second-round pick along with a 2011 seventh-round selection for third- and fourth-round picks this past draft to take offensive lineman Joe Barksdale and running back Taiwan Jones. They sent their fourth-round pick a year ago to the Redskins for Campbell.
The Associated Press contributed to this report.