The four faced prison terms of up to 72 years each if convicted of the charges that included "attempted terrorist killings" and "belonging to an armed organisation" at Madrid's National Court.
The court said in a statement that they could only prove that one of the accused, Luis Ignacio Iruretagoyena Lanz, known as "Suny", belonged to Eta but they acquitted him as he is already serving time in neighbouring France for the same crime.
"Suny" is suspected of having recruited the other three accused, but the court found that there was no evidence of their participation in the alleged plans and acquitted them too.
Eta is blamed for more than 800 killings in its campaign of bombings and shootings to create an independent Basque homeland in northern Spain and southwestern France.
In October 2011 it declared a "definitive end to armed activity" but it has yet to formally disband or disarm.
The four were accused of plotting three attacks against Aznar's plane in the northern Basque Country as he campaigned for regional elections.
But these allegedly failed as the missile launchers were defective.
Aznar, who served as conservative Popular Party prime minister between 1996 and 2004, was frequently an Eta target.
He survived an Eta car bombing in Madrid in 1995 when he was leader of the opposition. The car's armour plating protected him but one woman was killed and another 15 people were wounded.