Heap was set to become an unrestricted free agent following this season and had slipped to third on the depth chart after originally being slated as a starter in Arizona.
Cut by the Ravens after a decade in Baltimore, Heap signed a two-year contract with the Cardinals last year.
A Mesa, Ariz., native who starred at Arizona State, Heap was sidelined for six games with nagging hamstring issues during his first season with the Cardinals.
He accepted a paycut from $2.15 million to $1.15 million prior to this season.
Heap caught five passes for 62 yards against the New England Patriots in the second game of this season, but a posterior cruciate ligament knee injury suffered in that game effectively ended his tenure with the Cardinals.
In a dozen games with Arizona, Heap caught just 32 passes for 377 yards and one touchdown.
Heap was cut by the Ravens -- along with Derrick Mason and Kelly Gregg -- in a salary-cap move in 2011. Rather than pay him a $4.5 million salary last season, the Ravens elected to go with younger tight ends Ed Dickson and Dennis Pitta.
Heap was drafted by the Ravens in the first round in the 2001, eventually replacing Shannon Sharpe.
With the Ravens, Heap had 467 receptions for 5,492 yards and 41 touchdowns.
He was one of the most popular figures in franchise history and is regarded as a lock to enter the Ring of Honor.