NFL Network, which first reported the signing, says that Hicks will sign a four-year contract worth $36 million with a $12 million signing bonus and $20 million guaranteed.
The deal can't be officially announced until Wednesday at 4 p.m. ET when the 2019 league year begins.
Hicks becomes the second impact linebacker to agree to sign with the Cardinals, joining Terrell Suggs, who will sign a one-year, $7 million deal with Arizona, a source told ESPN's Adam Schefter.
Hicks' biggest issue in his four seasons with the Philadelphia Eagles was availability, as he missed 21 regular-season games due to a variety of injuries. He tore his Achilles midway through the 2017 season, and he was sidelined four games this past season with a calf strain.
Hicks, 26, has shown he can be an impact middle linebacker when healthy. In 2016, the only season he has played all 16 games, Hicks recorded five interceptions, 85 tackles, 12 tackles for loss and 11 passes defensed.
A former third-round pick out of Texas, Hicks has 254 tackles in 43 games with five sacks and seven interceptions.
ESPN's Tim McManus contributed to this report.