Napolitano commented on the news during a visit to the Slovenian capital of Ljubljana, where he was attending events marking the 20th anniversary of Slovenia's independence.
The Slovenian STA news agency quoted Slovenian Prime Minister Borut Pahor as describing the decision as very important for Croatia, the region and the EU.
According to the Slovenian media, Pahor congratulated Kosor on the decision and sent her a bunch of roses on that occasion.
Pahor said his country was very satisfied with those developments in light of expectations about the beginning of the arbitration process to settle the Croatian-Slovenian border issue following the completion of Croatia's EU accession talks.
Pahor voiced confidence about the strengthening of the friendship between the two countries.
Austrian leaders, too, welcomed the decision of the European Council, with Chancellor Werner Faymann welcoming the decision and describing it as an important signal to Western Balkans.
Austrian President Heinz Fischer extended congratulations to Croatian President Ivo Josipovic. The two presidents were in Ljubljana today, attending events marking the 20th anniversary of Slovenia's independence.