The trade is pending Hudson passing a physical, the Cardinals announced.
Hudson and Jackson were the second and third starting offensive linemen traded by the Raiders this offseason, joining tackle Trent Brown, who was dealt to the New England Patriots. Las Vegas also released guard Richie Incognito, but he tweeted Wednesday that he is re-signing with the team.
The team also agreed to re-sign offensive lineman Denzelle Good on Wednesday, sources told ESPN's Jeremy Fowler. Good started 14 games on the line last season.
Hudson will slide into the Cardinals' starting center role, replacing Mason Cole, who had the job in 2018 and 2020. Cole struggled at times last season and finished the year with four false-start penalties.
In Hudson, Arizona gets a veteran presence in the middle of the offensive line, plus someone who can provide leadership and guidance to third-year quarterback Kyler Murray. Cole could end up competing for the right guard job, which is the only position on the offensive line that hasn't been solidified for the 2021 season.
Arizona averaged 4.7 yards per carry last season, but its bid for a 1,000-yard rusher came up short when Kenyan Drake finished with 955 yards.
Hudson, who turns 32 in July, signed a three-year, $33.4 million extension, including $24.4 million guaranteed, with the Raiders on Aug. 30, 2019, which made him the highest-paid center in the NFL in terms of annual pay per year at $11.13 million a season. He restructured his contract for cap purposes last summer.
Hudson, a four-time winner of the Raiders' Commitment to Excellence Award as voted on by teammates, signed with the franchise as a free agent in 2015 after four seasons with the Kansas City Chiefs.
Pro Football Focus charged Hudson with three sacks allowed in 3,445 pass-blocking snaps with the Raiders. He missed just one game in six seasons with the team and was selected to three Pro Bowls.
A second-round pick of the Chiefs in 2011, Hudson has appeared in 143 games, including 127 starts, in his career.
Meanwhile, the Raiders also announced the signing of unrestricted free-agent defensive tackle Quinton Jefferson on Wednesday. He has 10½ career sacks and three passes defensed since joining the NFL in 2016. He has started 28 of his 55 career games.
ESPN's Josh Weinfuss and Paul Gutierrez contributed to this report.