Mr Kumar has been asked by Governor KN Tripathi to prove his majority in the Bihar Assembly on March 16
Nitish Kumar, who is set to return as Chief Minister of Bihar, on Friday described his decision to quit office last year as "a mistake".
"With folded hands, I apologise to the people of Bihar. Never again will I take such a step. I am ready to lead from the front," he said, after his rival Jitan Ram Manjhi quit as Chief Minister, hours before a trust vote in which the BJP had pledged to back him.
Mr Kumar will be sworn in on Sunday. He has been asked by Governor KN Tripathi to prove his majority in the Bihar Assembly on March 16.
West Bengal Chief Minister Mamata Banerjee, who had tweeted her congratulations to Mr Kumar on Friday, has said she would attend the swearing-in ceremony.
Mr Kumar's public contrition echoes the apology issued by Arvind Kejriwal when he was campaigning for the Delhi election. Mr Kejriwal had "begged for the people's forgiveness" for quitting as Chief Minister of the capital 49 days into his term. The remorse, expressed infrequently, had the desired effect. Mr Kejriwal and his Aam Aadmi Party or AAP won a record result, which has installed them in government once again.
Mr Manjhi was chosen by Mr Kumar to replace him after their party, the Janata Dal United or JDU, crash-landed in the national election last year, winning just two parliamentary seats.
Last month, Mr Manjhi was asked to step aside to allow Mr Kumar's return as Chief Minister as the party campaigns for the Bihar election due later this year. Mr Manjhi did not oblige, was expelled by the party, and sought a trust vote today. He quit abruptly when it was clear that he would not win.
The BJP's support to Mr Manjhi was motivated by the twin factors of his powerful standing within the Mahadalits, an extremely poor and under-privileged caste in Bihar, and Mr Kumar's status as the BJP's enemy number 1.
The BJP and the JDU aborted a lengthy alliance at the insistence of Mr Kumar ahead of the national election, a grave miscalculation for the then Chief Minister.