Penn's deal is worth $14 million, according to the San Francisco Chronicle.
Penn confirmed he was staying in Oakland via his Instagram account.
Penn, who turns 33 on April 27, reportedly was scheduled to visit the New York Giants later this week but that visit no longer will take place.
His return assures that Kelechi Osemele, who signed a five-year, $58.5 million contract with the Raiders on the first day of free agency, will play guard in 2016. Osemele has experience at tackle and likely would have replaced Penn on the left side had he signed elsewhere.
The Raiders now boast an offensive line that stands on average at 6-foot-4 and 319 pounds in left tackle Penn (6-5, 305), guard Osemele (6-5, 333), center Rodney Hudson (6-2, 291), guard Gabe Jackson (6-3, 336) and right tackle Austin Howard (6-foot-7, 333).
He has started 140 straight games, the third-longest active streak among offensive tackles in the NFL.
A Pro Bowl selection for Tampa Bay in 2010 who came to Oakland as a free agent in 2014, Penn has caught a pass in three straight seasons. He has caught three touchdown passes in his career, including a 3-yarder from Carr against the San Francisco 49ers in 2014.
ESPN NFL Nation reporter Paul Gutierrez contributed to this report.