The deal is worth up to $6 million, a source tells ESPN's Jeremy Fowler.
Butler will replace Patrick Peterson as the team's top cornerback option. Peterson, who played for the Cardinals all 10 years of his career, signed with the Minnesota Vikings last week. After the Cardinals let Peterson go in free agency, they were left with just two corners expected to play significant reps in Robert Alford and Byron Murphy.
Butler rounds out the Cardinals' starting cornerback rotation when they line up two outside and a slot corner.
By signing with the Cardinals, Butler will return to the stadium where he made one of the most memorable plays in recent Super Bowl history, intercepting Seattle quarterback Russell Wilson at the goal line in Super Bowl XLIX to clinch the Patriots' victory.
Butler signed a five-year, $61.25 million contract with the Titans in 2018 after spending four seasons with New England. He had signed with the Patriots as an undrafted free agent out of Western Alabama.
Butler, who turned 31 on March 2, spent three seasons with the Titans. He finished last season with four interceptions (tied for a career high), 14 passes defended and 100 tackles in 16 games. For his career, Butler has 17 interceptions, 5 forced fumbles, 3 sacks and 82 passes defended.
The two-time Super Bowl champion was selected to the Pro Bowl in 2015 and was named a second-team All-Pro in 2016.
ESPN's Turron Davenport contributed to this report.