Bradford started the first three games of the season before losing his job to rookie first-round pick Josh Rosen.
According to ESPN.com's Mike Sando, the Minnesota Vikings will lose a projected third-round compensatory pick in the 2019 NFL draft, while the Cardinals will gain a projected sixth-round pick by cutting ties with Bradford.
Following Carson Palmer's retirement, Arizona signed Bradford to a one-year, $20 million contract in free agency. Per Spotrac, the deal included a team option for 2019.
ESPN's Adam Schefter noted Bradford will land on waivers, and if a team claims him, it will inherit his Arizona contract:
In three starts with the Cards, Bradford went 0-3. He completed 62.5 percent of his passes for 400 yards with two touchdowns and four interceptions.
Bradford has been inactive for the past five games with a pectoral injury, and now that he's been released, veteran Mike Glennon will continue to serve as Rosen's backup.
Last season, a knee injury kept Bradford from appearing in all but two games for the Vikings.
The previous year, he set what was then an NFL record with a completion percentage of 71.6 percent and threw for 3,877 yards, 20 touchdowns and five interceptions.
He was selected with the No. 1 overall pick in the 2010 NFL draft by the St. Louis Rams and spent five seasons with the Rams before stints as a member of the Philadelphia Eagles, Vikings and Cardinals.
In 83 career starts, the 30-year-old Bradford is 34-48-1 with 19,449 yards, 103 touchdowns and 61 interceptions.
The Cardinals have struggled this season with the third-worst record in the NFC at 2-6.
Arizona is on a bye week, but Rosen is expected to be under center when it travels to Kansas City to take on the Chiefs next Sunday.