Gresham, 27, turned down contracts of up to four years for $23 million with $12 million fully guaranteed from other teams because he wanted to be back in Arizona, according to ESPN.
"Just that he loves the culture of our football team and what we speak for," Cardinals head coach Bruce Arians recently said of Gresham.
The 6-foot-5, 260-pound Gresham played in 15 regular-season games (12 starts) and both postseason contests last season, with 18 catches for 223 yards and a touchdown. As a run blocker, he helped Arizona finish eighth in the NFL in rushing in 2015, averaging 119.8 yards per game.
Gresham is a two-time Pro Bowl selection (2011-12) who spent his first five seasons in the league with the Cincinnati Bengals after he was selected in the first round (21st overall) out of Oklahoma in the 2010 NFL Draft. Gresham played in 74 games (67 starts) in five seasons (2010-14) with the Bengals and had 280 receptions for 2,722 yards and 24 touchdowns.
The 6-4, 323-pound Bryant played the final six games of the season last year for the Cardinals after signing with the team on Nov. 26. He is an eight-year NFL veteran who began his career with the Seattle Seahawks as a fourth-round selection in the 2008 draft out of Texas A&M.
Bryant, 31, played his first six seasons with the Seahawks (2008-13) before starting all 16 games with the Jacksonville Jaguars in 2014. In his career, Bryant has played in 86 games (71 starts), collecting 147 tackles, 4.5 sacks, two forced fumbles, two fumble recoveries, two interceptions, seven passes defensed and 14 tackles for loss. He has blocked four kicks in his career -- three field goals and one extra point.