Banerjee, who held a 30-minute one-to-one meeting with the Bangladeshi prime minister on the concluding day of her three-day visit to Dhaka, described Hasina as her "favourite didi".
"Today I had the privilege to call upon, the Honorable Prime Minister of Bangladesh, Sheikh Hasina ji who is my favourite didi," she tweeted.
"I invited Honorable Prime Minister to visit West Bengal," she said in another tweet.
The West Bengal chief minister said Hasina's "warmth and grace made me emotional."
Banerjee, who arrived here on Thursday on her first visit since assuming office as the Chief Minister of West Bengal in 2011, has said she was keen to respond to Bangladesh's expectations" from West Bengal.