The deal was reported earlier Monday by the NFL Network.
Hudson, 25, was graded by Pro Football Focus as best among Chiefs offensive linemen in 2014 and was PFF's third-rated center in the league.
He joined the Chiefs in 2011 as a second-round draft pick from Florida State and became their full-time starting center in 2013. Hudson sat out most of 2012 with a leg injury but has been durable since.
His lone missed start over the past two seasons was the final regular-season game of 2013, when the Chiefs rested many of their starters.
Oakland's addition of Hudson likely signals the end of center Stefen Wisniewski's tenure with the team.
Wisniewski, the nephew of former Raiders star offensive lineman Steve Wisniewski, is scheduled to become a free agent when the new league year begins Tuesday.
The 25-year-old Wisniewski played his first four seasons with the Raiders and has appeared in 61 games -- all starts.
ESPN.com Chiefs reporter Adam Teicher contributed to this report.