The meeting at the presidential palace in the capital was captured on camera and appears to show Bana thanking Erdogan in English, saying: "Thank you for supporting the children of Aleppo and help us to get out from war. I love you."
Her story caught the attention of Erdogan and Turkish Foreign Minister Mevlut Cavusoglu, who spoke with the child on Twitter and encouraged her to stay strong.
Bana took to Twitter during the siege of eastern Aleppo to share her experiences, which were written by her mother, Fatemah, an English teacher.
She has nearly 360,000 followers on the social network and tweeted after the meeting of how happy she was to meet with the President.
Turkey's involvement in Syria is complicated
. On one hand, the Turks are eager to help eradicate ISIS. On the other, Ankara has worked to drive Kurdish fighters from the Syrian side of the border, fearing that an entrenched Kurdish canton there would fuel momentum for an independent Kurdish state that could claim Turkish territory.
The video of the meeting has been posted to the official Twitter account of Hasan Dogan, the chief of the cabinet of Erdogan.
Erdogan later tweeted: "I was pleased to host @AlabedBana and her family at the Presidential Complex today. Turkey will always stand with the people of Syria."
Bana's mother had appealed directly to Turkey to end the siege of eastern Aleppo and help those trapped inside escape.
There are 172 Aleppo evacuees, including 68 children, now undergoing treatment at Turkish hospitals, Turkish state news agency Anadolu reports, quoting the Directorate General of Press and Information on Wednesday.
The injured, particularly those in critical condition, had been transported to hospitals in Turkey's southeastern Hatay province, Anadolu said. The ongoing evacuation of eastern Aleppo has been facing delays.
'Girl who announced Aleppo'
Describing Bana as the girl "who announced the Aleppo massacre to the world on social media", Cavusoglu told Anadolu that she and her family would be brought to Turkey earlier this month.
Bana has two brothers -- Mohammed, 5, and Noor, 3 -- along with her mother and father. The young pig-tailed, gap-toothed girl kept a harrowing log of the conflict on Twitter with the help of her mother.
Following the evacuation, mother Fatemah spoke of her sadness at leaving Aleppo, saying she had "left her soul" in the besieged city.
"When we got out we had a lot of suffering because we stayed almost 24 hours in bus without water and food or anything ... like a prisoner," she told the pro-opposition media organization Qasioun News.
"But finally we arrived here and we thank God and all our friends who are supporting us."
Three months ago, Fatemah decided she wanted the world to hear her children's voices and see their faces, hoping that maybe she could galvanize global support for those in Aleppo.
Bana has since become an embodiment of the human toll this grinding conflict has had on the children of Syria.
Bana's family went into hiding after their home was reduced to rubble on November 27. More than three weeks later, on December 19, Bana tweeted that they had "escaped" from eastern Aleppo.