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 charges 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.
Amnesty International: Terrorism verdict for Facebook posts is a shameful affront to freedom of expression
In response to news that former Ethiopian opposition spokesman Yonatan Tesfaye has been found guilty of “encouragement of terrorism” in connection with his posts on Facebook, Michelle Kagari, Amnesty International’s Deputy Regional Director for East Africa, the Horn and the Great Lakes, said:
“Today’s verdict is a miscarriage of justice. It is yet another example of how the Anti-Terrorism Proclamation is used to target and destroy people who criticize the government. All Yonatan did was express himself online. This is not a crime, yet he now faces up to 20 years in jail under this draconian and deeply-flawed law.
“This ruling is a shameful affront to people’s right to express themselves and further entrenches repression in Ethiopia.”
Yonatan, a former senior official in the opposition Semayawi (Blue) Party, was arbitrarily arrested in December 2015 for comments he posted on Facebook, in which he criticized the government’s response to protests in the Oromia region.
He will be sentenced on 25 May.