"Responding to his request, I agreed to attend the ceremony,," the Trinamool Congress chief said.
She also invited him to visit West Bengal first after winning the elections.
Party sources said Banerjee would be leaving for the capital on July 24 and return here on July 25 after attending the ceremony.
TMC MP Kunal Ghosh said Mukherjee told the chief minister during the telephonic talk that his win would have been incomplete without the support of the Trinamool Congress.
Banerjee, who had initially opposed the candidature of Mukherjee, had announced her party's support to him two days before the election on July 19.