Financial terms of the deals were not disclosed by the Cardinals, who also released defensive end Praise Martin-Oguike with a waived/injured designation.
The 30-year-old Moats spent appeared in 14 games with Pittsburgh in 2017, his fourth season with the Steelers and eighth in the NFL. Moats had only five tackles and did not register a sack last season after recording 11.5 in his first three years with Pittsburgh.
He spent his first four seasons with Buffalo after the Bills selected him in the six round of the 2010 NFL Draft. In 121 career games (45 starts), the 6-foot, 246-pound Moats has 191 tackles (112 solo), 16.5 sacks, four forced fumbles, four fumble recoveries and six passes defensed.
Smith appeared in a combined three games with Tampa Bay and Detroit last season, making only one tackle before he was cut by the Lions in mid-November.
The 6-2, 260-pound Smith spent his first three seasons with the Buccaneers, starting a combined 18 games in 2014 and 2015 and amassing 13.5 sacks in those two years. He was signed as an undrafted free agent by Miami in 2012.
Martin-Oguike has not played a down in the NFL. He has 17.5 sacks in four seasons at Temple, including a career-best 7.5 as a senior in 2016.