Club Olimpia made the announcement on their verified Twitter handle on Tuesday.
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The club will compete in this year’s Copa Libertadores (South American Champions League) and have won the competition three times.
They have emerged winners of the Paraguayan Primera Division (top-flight) 44 times in their history.
Adebayor, 35, was a free agent after ending a brief spell with Turkish side Kayserispor in December.
Adebayor established himself in Turkey by scoring 30 goals in 76 appearances for Istanbul Basaksehir and eight for Kayserispor.
He had previously played for clubs like Metz and AS Monaco in the French Ligue 1.
During his loan spell at Real Madrid, Adebayor won his only silverware at club in 2011 when they Barcelona 1-0 in the final of the Spanish Copa del Rey.
He was named the 2007 BBC African Footballer of the Year and the CAF African Player of the Year the following year.
He remains Togo’s all-time top scorer with 32 goals and played for them at their only World Cup appearance in 2006.
Also, he has represented his country at four Africa Cup of Nations in 2002, 2006, 2013 and 2017.
And his last appearance for Togo was in a 2-1 away defeat to neighbours Benin in March 2019 in a 2021 Africa Cup of Nations qualifier.
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