The Gazi Husrev-beg library houses more than 100,000 items, the oldest being an Arabic-language handwritten manuscript dating to 1106.
During the 1990s inter-ethnic war in Bosnia and siege of Sarajevo, the collection had been hidden, with 500 of the most valuable manuscripts and books locked up in a bank vault.
To eliminate the threat that the items could one day be lost, "all manuscripts are digitised and copies are saved at three different places around the world," said Ahmed Alibasic, who chairs the library's management board.
"The knowledge is a gift from God and our task is to transfer it," Bosnia's grand mufti Husein Kavazovic said at an official opening ceremony, attended also by Qatar's Minister for Religion and Islamic affairs Ghaith Bin Mubarak Al-Kuwari.
Qatar donated some USD 8.8 million towards the construction of the library, which is named after one of Sarajevo's founders who had constructed the first library in the Bosnian capital in 1537.
Bosnia was part of the Ottoman Empire from 1463 to 1878 and more than 40 per cent of its 3.8 million inhabitants are Muslims.