Turkey faces competition from France and Italy, both of which have hosted European Championships and two World Cups each. UEFA is due to announce its decision in Geneva on May 28.
"Turkey is applying to host the championship for the third time and this is the best sign of our determination ... we are ready to give our all to provide an environment where Europe's best teams will play the best football," Erdogan told UEFA officials at a reception in Istanbul.
According to its bid proposal Turkey would build six new stadiums in Ankara, Izmir, Bursa, Konya, Antalya and Eskisehir, and renovate a stadium in Kayseri.
Istanbul's Olympic Stadium would be renovated and Galatasaray's new stadium, currently under construction, would also be used.
"I, as Prime Minister of Turkey, have presented you with a letter of guarantee worth 920 million euros," Erdogan told UEFA, adding other ministers had given additional guarantees.
Turkey has never hosted a major football tournament but Erdogan, an avid footballer in his youth, pointed out that Istanbul had hosted the 2005 Champions League final between Liverpool and AC Milan, won by the English side on penalties.
"Many people think that was the best Champions League final ever, which gives me the confidence to promise you the best European championship ever held," he said.
UEFA has said more than 100 criteria, from stadiums and accommodation to legal matters would be examined in considering where to hold the tournament.
It will be the first European Championship to feature 24 teams, eight more than will compete in 2012 when Poland and Ukraine co-host the event.
Sweden and Norway had also put forward a joint candidature for Euro 2016 but withdrew in December after their governments said they would not be providing the money needed for investment in stadiums.
Erdogan stressed Turkey's reputation for hospitality and the country's improving transport infrastructure.
"Not only I, but the whole Turkish nation is very excited about May 28 when the results will be announced."
