Hoyer would have cost a team a second-round draft pick as a result of his tender if he was signed to an offer sheet during the period to sign restricted free agents. He was scheduled to make $2,023,000 in 2013.
The 27-year-old Hoyer, who spent three seasons as a backup to Tom Brady in New England, was claimed on waivers by the Cardinals late last season and started the team's season finale, becoming the fourth quarterback to start for Arizona in 2012.
He finished last season with 330 yards, with one touchdown and two interceptions, completing 30 of 53 pass attempts in two games.
The Cardinals, however, traded for Carson Palmer and signed Drew Stanton this offseason, pushing Hoyer down the depth chart at quarterback. Arizona also has Ryan Lindley, who was drafted by the team in 2012, at the position.
The Cardinals also announced they have signed second-round pick Kevin Minter, as well as center Adam Bice and quarterback Caleb TerBush.
The Cardinals used the 45th overall pick in this year's draft to select Minter, a linebacker from LSU who was a finalist for the Butkus Award for the nation's top linebacker.
Bice and TerBush were undrafted rookie free agents who participated in Arizona's rookie minicamp last week.
Information from The Associated Press was used in this report.