The 36-year old has fallen out of favour at Bundesliga club Hamburg and has also been overlooked by Croatia coach Ante Cacic in the run-in to the June 10-July 10 tournament in France.
"I thought about it a lot and realised I shouldn't immerse myself where I don't belong," Olic, who scored 20 goals in 104 appearances for his country, told Croatian media.
"I told Cacic openly I was upset about being left out of the 3-1 win over Russia (in a friendly last November), but he remained adamant that players not featuring for their clubs had no place in the national team."
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Olic, who made his international debut in 2002, is Croatia's fourth most capped player behind captain Darijo Srna, goalkeeper Stipe Pletikosa and retired defender Josip Simunic.
After leaving the Croatian first division in 2003, he played for CSKA Moscow, Bayern Munich, Wolfsburg and has had two stints with Hamburg, rejoining them last year.
"Croatia has always been everything to me and I will be the team's biggest fan at Euro 2016," he told the Croatian Football Associaton's website (www.cff-hns.hr).
The Croatians are in Group D alongside holders Spain, Turkey and the Czech Republic.
(Writing by Zoran Milosavljevic in Belgrade, editing by Alan Baldwin)
