Ramadan, 55, paid the Belgian-Moroccan woman 27,000 euros to stop posting details about their affair online, Luc Hennart, president of the Court of First Instance in Brussels, confirmed to the AFP news agency on Wednesday.
The Oxford professor was detained by a French court in February over charges that he raped two Muslim women in France.
A third woman has since made further allegations of rape. Ramadan denies all the charges.
Hennart said a public judgment was made in Brussels in May 2015 between the professor and the woman, Majda Bernoussi, after she posted online about his "psychological grip" on her.
She did not accuse him of rape or sexual assault.
The agreement "provides that Majda Bernoussi deletes her online posts and stops publishing new ones, for a sum of money given by Tariq Ramadan," Hennart said.
Bernoussi also agreed to no longer send "offensive or threatening messages" to the professor and his family, according to French news website Mediapart.
Ramadan's two accusers in France went to the police in late October, both alleging that he had raped them in French hotel rooms.
A professor of contemporary Islamic studies at Oxford, Ramadan has been on leave since November after the allegations emerged.
One of European Islam's best-known figures, he has dismissed the accusations against him as a smear campaign by his enemies and his lawyers argue there are inconsistencies in the women's accounts.