Knapp will replace Al Saunders, the lone assistant from former coach Hue Jackson's staff still under contract.
This will be Knapp's second stint in charge of Oakland's offense. He served as offensive coordinator in 2007 and 2008 under Lane Kiffin.
When Tom Cable took over as interim coach after Kiffin was fired in 2008, Cable stripped Knapp's duties from him. In Knapp's only full season as the offensive coordinator (2007), the Raiders were No. 27 in total offense.
Dennis Allen, who had just one year of experience as a defensive coordinator in Denver, was introduced as Oakland's head coach Monday.
Allen said Monday he wants to run an up-tempo, aggressive offense and believes he has many of the playmakers needed to make it work. Carson Palmer will be back for his first full season with the Raiders and has already talked to Allen and new general manager Reggie McKenzie about the new direction for the franchise.
"Carson Palmer is extremely excited about what we have going here," Allen said. "He's looking forward to the future and he's excited about the opportunities here."
McKenzie said Monday that Allen could keep a few of the other assistants from Jackson's tenure but most of the staff will be new.
The Raiders were denied permission by Denver to interview Broncos linebackers coach Richard Smith for Oakland's defensive coordinator job, a source told Schefter.
Information from ESPN.com's Bill Williamson and The Associated Press contributed to this report.