Venezuelan authorities detained Jose Ignacio Echarte and two other suspected ETA members in August after the boat they were in ran aground on the Venezuelan island of Los Roques, just south of Cuba.
They then turned him over to Cuban authorities.
The extradition request is based on information found on computer archives seized from three ETA leaders in Paris in 1999 which allegedly showed Echarte had requested permission to work with explosives, Spain`s justice ministry said in a statement.
"Echarte requested permission to take part, with several members of FARC, in the launch of grenades and mortars in the Colombian-Venezuelan jungle," it said.
Spain`s National Court Judge Eloy Velasco, who has been investigating suspected ties between ETA and the Revolutionary Armed Forces of Colombia (FARC), had issued an international arrest warrant for Echarte and requested his extradiction from Cuba.
The government approved Justice Minister Francisco Caamano`s decision to file the extradiction request for Echarte at a cabinet meeting on Friday, the justice ministry statement said.
ETA is held responsible for 829 deaths in its battle to carve out an independent Basque homeland in northern Spain and southwestern France.
FARC is the oldest and largest leftist guerilla group in Colombia with an estimated 8,000 combatants. (M014)