The 45-minute meeting at the Writers' Buildings was the first interaction between the two chief ministers.
Yadav, who was here to attend the Samajwadi Party's national executive, said, "It was necessary to meet her."
Banerjee he said, "I understand the government here is working as per the aspirations of the people. After a lot of struggle, she has come to power. I thank her for finding time for me."
Banerjee said she has discussed some new schemes being taken up by the Uttar Pradesh government and which the state government in West Bengal have also implemented.
"Many things have been cleared up through interactions and we will meet again," she said.