Corporal Francisco Javier Soria Toledo was hit by Israeli artillery following a Hezbollah attack which killed two Israeli soldiers, according to a military statement.
The 36-year-old UN peacekeeper was killed near the village of Ghajar, in the Shebaa Farms area, on 28 January.
The Israeli military said there had been no intention to harm UN troops.
Hezbollah said at the time that its attack on the Israeli soldiers was retaliation for an air strike that killed six Hezbollah fighters and an Iranian Revolutionary Guards general in the Syrian Golan Heights 10 days earlier.
Cpl Soria was part of the United Nations Interim Force in Lebanon (Unifil), which is made up of more than 10,000 troops from 38 different countries.
A Spanish soldier who was killed in Lebanon in January died as a result of Israeli fire, Israel's military says.