However, Benarbia's departure brought forward the move, costing City £750,000.
"The minute Ali said that he was going we picked this up much quicker than we had intended to," the City boss told the club's official site.
"We had been looking to do the deal for next season when Ali finished so we just fetched it forward. "Antoine was in his final year of his contract and would have been a Bosman so within the rules we could have tied him up in January.
"This way we have paid around £750,000 for him but it is worth it. He is another quality player coming to the club."