Cleveland waived Harrison on Wednesday after he missed the start of the Browns' mandatory veteran minicamp.
Arizona had the first crack at Harrison since it owns the No. 1 spot in the waiver wire order.
After going undrafted in 2018, Cleveland signed Harrison as a rookie free agent out of West Georgia. Not only did Harrison make the team, but he earned the starting job at left tackle out of training camp.
As the replacement for future Hall of Fame left tackle Joe Thomas, Harrison started the first eight games of the season. After head coach Hue Jackson was fired and replaced by Gregg Williams on an interim basis, however, 2014 No. 2 overall draft pick Greg Robinson took over as the starter.
With Robinson back as quarterback Baker Mayfield's blindside protector for 2019, Harrison would have merely been a backup swing tackle in Cleveland.
In Arizona, Harrison will likely start behind left tackle D.J. Humphries and right tackle Marcus Gilbert, but given the amount of turnover the Cardinals have experienced on the offensive line since last season, he may have an opportunity to compete for a starting job during training camp and the preseason.
If Harrison does win a starting spot, he will have the honor of blocking for the No. 1 overall draft pick for the second consecutive season, as the Cards took quarterback Kyler Murray with the top pick in the 2019 NFL draft.