Conner was given a fully guaranteed $1.75-million contract with a $500,000 signing bonus, ESPN's Adam Schefter reports.
Conner, who is recovering from offseason toe surgery, visited the Cardinals on Monday.
The 25-year-old suffered the injury while riding in a recreational vehicle this offseason but is expected to be fully recovered by June, according to Ian Rapoport of NFL Network.
Conner racked up 973 rushing yards and 12 touchdowns for the Pittsburgh Steelers in 2018 to earn his first career Pro Bowl nod. However, his production fell off over the next two seasons and the Steelers didn't re-sign him.
Arizona needed to add to its backfield after Kenyan Drake signed with the Las Vegas Raiders in free agency. Conner will likely split time with Chase Edmonds, who had a career-high 850 yards from scrimmage last season as Drake's backup.
Conner was diagnosed with Hodgkin's lymphoma while playing at the University of Pittsburgh in 2015. He was declared cancer-free the following year and the Steelers selected him in the third round of the 2017 NFL Draft.