Turk Telekom, a state-run monopoly until it was privatised in 2005, provides internet services for the vast majority of Turkish internet users.
Now, those navigating to YouTube's website from Turkey are greeted with the message: "Access to this site has been blocked by a court decision".
Over the past week, Turkish media has publicised arguments between Greeks and Turks who are using YouTube to post videos belittling and berating each other.
The CNN-Turk Web site featured a link allowing Turks to complain directly by email to YouTube about the "insult".
On its front page on Wednesday, the Hurriyet newspaper said thousands of people had written to YouTube and that the Ataturk videos had been removed from the site.
"YouTube got the message", read the headline.
Doany has said Turk Telekom would allow access to the popular video sharing site again if the court decision were rescinded.
After a petition by Turk Telekom, the court later ruled that it would revoke its ban once it ascertained that the offending videos had been removed from YouTube.
Insulting Ataturk or "Turkishness" is a crime in Turkey punishable by a prison sentence.