The Algeria international was handed a three-match ban by the FA for violent conduct after he was caught on camera kicking West Bromwich Albion defender Craig Dawson.
The attacker has endured a difficult time at the St James' Park outfit since he joined in January, featuring in only four league games owing to injury.
And manager Rafael Benitez has revealed that he allowed the former Sporting CP player to leave since he will not take part in their remaining games of the season.
“I said he can go because he will not be part of the team in these two games,” Benitez told Chronicle Live.
“We told [Slimani] that he can go if he wants, and he has.”
The former Liverpool boss also disclosed that the forward apologised for the behaviour that brought his Magpies career to an abrupt end before his departure.
“Yes [he apologised]. He was not very happy obviously. He knows that he made a mistake,” he continued.
“I was talking with him today when he was leaving. He has the energy and he was running behind defenders, he was working hard trying to do things in the way he knows he has to do it. I was telling him I like that.”