Jha was 86 and is survived by his wife, a son and two daughters, family sources said. (Agencies)
He was Chairman of the Upper House between 2009 and 2012.
In a distinguished political career spanning over three decades, Jha was one of the founding members of BJP and also headed the state party unit.
Denied renomination to the Legislative Council last year, Jha quit BJP to join JD (U) earlier this year.
An eminent jurist, Jha held the position of Advocate General of Bihar and also served with distinction as the Chairman of Bihar Bar Council and member of the Bar Council of India.
He had also played a major role in inclusion of Maithili in the 8th schedule of the Constitution to give the language an official status.
Chief Minister Nitish Kumar expressed profound grief over his demise.
His death has caused a huge void in polity and society, Kumar said in a condolence message and described the departed leader as an eminent jurist and dedicated politician.
Bihar Legislative Council Chairman Awadesh Narayan Singh, Leader of Opposition in the Legislative Council Sushil Kumar Modi and leaders of various political parties paid tributes to the departed leader.
Jha was 86 and is survived by his wife, a son and two daughters, family sources said.