Mukherjee's name was cleared by a three member assembly committee comprising Banerjee, Speaker Biman Banerjee and Leader of Opposition Surjya Kanta Mishra.
While the chief minister proposed Mukherjee's name, it was seconded by the speaker. Despite Mishra raising objection over the need to appoint a retired police officer in the panel, he was overruled by majority.
The recommendation will now go to Governor M.K. Narayanan.
Mukherjee, who retired as director general of police last month, is regarded as Banerjee's yes man.
Two of the commission members - Justice (retd.) Narayan Chandra Sil and former state chief secretary Sourin Roy are set to complete their terns Nov 1 and Nov 15 respectively.
As per rules, a retired judge has to replace Sil.
Once the governor approves, the decks would be clear for Mukherjee to replace Roy in the category of a member "appointed from amongst persons having knowledge of, or practical experience in, matters relating to human rights".
Mishra later told media persons he objected to Mukherjee taking over the job as the Supreme Court had earlier ruled that police officers cannot be made members of human rights panels.
"No policeman was ever appointed by the Left Front government (which preceded the current regime in the state) as a member of the commission. The Supreme Court has also ruled that police personnel cannot be member of national or state human rights panels.
"Also, the slot which Mukherjee will fill in falls vacant later. The vacancy for the other post arises on Nov 1. So why is the government in a hurry to take a decision on this post now?"Mishra also argued that the commission was probing several complaints where the state police was the accused.
"Mukherjee has just retired as DGP. He was at the helm as DGP during some of these cases. It is not desirable that the person against whom the accusations have been filed will investigate these cases."
Several orders passed by the panel have irked the Banerjee government, while the panel head, retired Supreme Court judge Asok Kumar Ganguly, has also launched scathing attacks on the Trinamool regime on a number of occasions alleging "rise in disorder".
The WBHRC earlier ordered the state government to pay compensation to Jadavpur University professor Ambikesh Mahapatra and his neighbour who were arrested for circulating emails mocking Banerjee.
It also directed the government to pay compensation to a farmer who was dubbed by the chief minister as a Maoist and arrested by the police after he asked her about the rising price of fertilisers at a public rally.