Turkish Football Federation (TFF) head Yildirim Demiroren handed over the application to Theodore Theodoridis, UEFA's General Secretary.
Demiroren said Turkey "deserves" to host the event after three failed bids for previous football championships.
The TFF announced it was bidding to host EURO 2024 on Feb. 15.
The 17-member UEFA executive committee selects hosts for the international tournament.
Along with Turkey, Germany and a combination of Nordic countries including Norway, Sweden, Denmark and Finland have also confirmed bids to host Euro 2024.
The application deadline ends on Friday.