Alexander is the second former Vikings cornerback to agree to join the Bengals after Trae Waynes agreed to a three-year, $42 million contract, per ESPN and NFL Network.
The Bengals will have a reshuffled cornerback rotation next season after losing cornerback Darqueze Dennard in free agency after he agreed to a deal with the Jaguars, sources told ESPN's Adam Schefter, and Cincinnati also released corner B.W. Webb, who started 12 games last season.
As for the Vikings, Mike Hughes could be in line to replace Alexander in the slot, if needed, or move to one of the starting outside spots. Minnesota also has Holton Hill and Kris Boyd on the roster, but coach Mike Zimmer now will need to address the position high in the draft.
After Alexander built a reputation in two seasons at Clemson as a physical outside cornerback, the Vikings drafted him 54th overall in 2016 with the intention of moving him to the slot.
The 5-foot-10 defensive back transitioned slowly as a nickel corner, eventually taking over the position left vacant by Terence Newman two years ago. But it was his play during a contract season in 2019 when Alexander's efforts finally caught on.
The cornerback allowed a 90.2 passer rating into his coverage in 2019. During a meaningless Week 17 loss to Chicago in which many of the Vikings' starters did not play, Alexander sustained an injury to his knee that required offseason surgery, forcing him to miss Minnesota's postseason run.
Alexander, 26, has 2 interceptions, 4.5 sacks, 21 passes defended and 9 tackles for loss in four seasons.
ESPN's Ben Baby and Courtney Cronin contributed to this report.