He was arrested in December 2015 as a wave of anti-government protests in the Oromia region was gathering momentum.
The authorities objected to several posts including one in which he said the government used "force against the people instead of peaceful discussion".
Ethiopia has been criticised for using anti-terror laws to silence dissent.
Amnesty International described the charges as "trumped up", when they were confirmed in May 2016.
A section of Ethiopia's anti-terror law says that anyone who makes a statement that could be seen as encouraging people to commit an act of terror can be prosecuted.
In a translation of the charge sheet by the Ethiopian Human Rights Project that details the Facebook comments, Mr Yonatan allegedly said: "I am telling you to destroy [the ruling party's] oppressive materials... Now is the time to make our killers lame."
Mr Yonatan, who was a spokesperson for the opposition Blue Party, is due to be sentenced later this month and faces up to 20 years' imprisonment.
The government faced unprecedented protests from November 2015 as people in the Oromia region complained of political and economic marginalisation.
The protests also spread to other parts of the country.
More than 600 people died in clashes between security forces and the demonstrators as the authorities tried to deal with the unrest, according to the state-affiliated Human Rights Commission.
The government introduced a state of emergency last October to bring the situation under control.
Opposition leader Merera Gudina was arrested last December for criticising the state of emergency and he is still being held.
Ethiopian opposition politician Yonatan Tesfaye has been found guilty of encouraging terrorism for comments he made on Facebook.