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The 35-year-old Togolese striker was welcomed by hundreds of fans earlier this month when he arrived in Asuncion.
Olimpia treasurer Miguel Brunote said at the time that Adebayor was commanding the biggest ever salary in Paraguayan football.
Adebayor, the 2008 African player of the year, was introduced at half-time of Olimpia's 1-1 draw with Cerro Porteno.
He had been without a club since the termination of his contract with Turkish club Kayserispor in December.
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Adebayor's former clubs include Arsenal, Tottenham Hotspur and Real Madrid, while he was also a Champions League runner-up with Monaco in 2004.
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