The newspaper added that the dismissed were deputy governor of the bank, Semih Toman and Ugur Namek, as well as a member of the Monetary Policy Committee, Abdullah Yavas.
Erdogan appointed Taha Cakmak as deputy governor of the Central Bank and Yusuf Tuna as a member of the Monetary Policy Committee.
After the announcement, the Turkish lira fell to a new record low of 9.19 against the dollar, bringing its losses since the beginning of the year to 19% due to monetary policy concerns.
And the Turkish presidency announced yesterday evening, Wednesday, that Erdogan had met the Governor of the Central Bank, Shehab Kavcioglu, and published a picture of the two of them standing next to each other.
The central bank last month cut the key interest rate to 18% from 19%, despite annual inflation rising to around 20%, in a move analysts saw as fresh evidence of political interference from Erdogan, who describes himself as an enemy of interest rates.
Kavcioglu said this week that the rate cut was not a surprise and had nothing to do with selling the lira later.
The Monetary Policy Committee of the Central Bank will hold its next meeting on the 21st of this month.
Informed sources told Reuters last week that Erdogan is losing confidence in Kavcioglu less than 7 months after his predecessor was ousted, and that there has been little contact between the two in the past weeks.
Erdogan has made changes in the Monetary Policy Committee over the past years, dismissing 3 governors in the past two and a half years, which has severely affected the lira.
The headline inflation rate reached its highest level in two and a half years at 19.58% in September.
Erdogan appointed Kavcioglu in March after ousting Naji Iqbal, after raising interest rates to 19%.
Erdogan ramped up pressure to cut interest rates in June when he said he had spoken to Kavcioglu about the need to cut rates after August.