Cleo, who scored 12 goals in 24 appearances for Red Star last season, followed in the footsteps of former Yugoslavia midfielder Goran Milojevic.
He said he expected Red Star fans, whose intense rivalry with Partizan supporters has often erupted into the most violent crowd trouble, to "understand and accept" his decision.
"No one has said anything bad to me yet nor has anyone made any threats," Cleo told reporters after signing a four-year contract with Partizan.
"Red Star fans know their club's financial situation, we could not reach an agreement and there is nothing malicious in what happened.
"The key to my decision was the fact that Partizan won the Serbian league title and will be aiming to reach the Champions League group stage next season."
ILIC ATTACK
Earlier this month, three Red Star fans were arrested after attacking Partizan's former captain Sasa Ilic and his pregnant wife in a Belgrade restaurant.
Daily papers had said Cleo might need bodyguards for him and his family if he made the switch but Partizan coach Slavisa Jokanovic rubbished the suggestions.
"It is absolutely ridiculous, such implications can only galvanise the fans and it would be in everybody's best interest to show some maturity," Jokanovic said.
"Red Star could not keep him, he is a committed professional and we signed him because we are confident that he will be a real bonus to our squad.
"I hope he scores six goals against Red Star in the next Belgrade derby."
Red Star, the 1991 European Cup winners, are going through a serious financial crisis and have been forced to release many of their regular starters.
Their debts to players and creditors have soared to 30 million euros and at one point last season they had water and telephone supplies cut off over unpaid bills.
