By Agence France-Presse
Erdogan hugged the girl emotionally and also held Bana and her brother as they sat on his knees flanked by the president's wife Emine.
"Very happy to meet with Mr Erdogan," Bana wrote on a tweet above a picture of her nestling up to the cheek of the smiling Erdogan.
The young Syrian girl was one of thousands of people evacuated from once rebel-held areas of Aleppo in the last days under a deal brokered by Turkey and Russia.
She was evacuated on Monday and Turkish officials promised then she would come to Turkey with her family. But it was not clear when she had crossed over.
"Thank you for the help in saving the children of Aleppo from the war. I love you very much," Bana told Erdogan according to the presidency.
'Stand by Syria'
For her 330,000 online followers, Bana is a symbol of the tragedy unfolding in Syria, although Syrian President Bashar al-Assad's regime has slammed her and her mother's nearly daily tweets as propaganda.
Her mother Fatemah, who runs the account @AlabedBana, was also in attendance on Tuesday, the Turkish presidency said.
"I was pleased to host @AlabedBana and her family at the Presidential Complex today," Erdogan said in his own tweet.
"Turkey will always stand with the people of Syria," he added.
Turkey is hosting some 2.7 million refugees from the Syria conflict but has made clear it now prefers to look after those recently displaced, who are not injured, on the Syrian side of the border.
However it makes exceptions for special cases and the wounded. It was not immediately clear if Bana would be staying in Turkey.
Bana's account has posted pictures of the destruction in Aleppo including her rubble-littered street, while people have tweeted messages of support and concern, notably fearing for her life when tweets became less frequent.
At least 15,000 children are among the more than 300,000 people who have been killed in Syria's near six-year war.
In her last tweet with her mother Fatemah before the evacuation, Bana made an appeal to Erdogan and Turkish Foreign Minister Mevlut Cavusoglu to put a fragile ceasefire back on track after frequent delays.
"We have brought the hope and symbol of the children of Aleppo, Bana, and her family to our country," tweeted Cavusoglu. "What could be more beautiful than the smile of a child?."