Pakistan's Prime Minister Zafarullah Khan Jamali has resigned following a meeting with the country's President, Pervez Musharraf.
Jamali picked Hussain to succeed him
Mr Jamali confirmed his resignation and nominated ruling party president Chaudry Shujat Hussain as successor.
The BBC's Paul Anderson in Islamabad says the Cabinet will also resign but remain in a caretaker capacity until a new prime minister takes office.
The news followed weeks of speculation in media and political circles.
The prime minister's resignation came on the eve of new talks between India and Pakistan over the disputed territory of Kashmir - the first meeting between the neighbours on the issue for three years.
Mr Jamali made his announcement at a meeting of the ruling Pakistan Muslim League (PML) parliamentary group.
"I resigned from my post as prime minister today," he told reporters. "Long live Pakistan."
Earlier in the day, Mr Jamali told President Musharraf he was stepping down.
He said he had been "authorised" to announce Chaudry Shujat Hussain's name.
Mr Jamali said Mr Hussain would face a mandatory vote of no confidence in parliament - where the PML enjoys a commanding majority - on Monday.
Mr Hussain paid tribute to Mr Jamali, saying "His name will go down in the history in golden words."
But our correspondent says many of Mr Jamali's 19 months in office were dogged by accusations of ineffectiveness and nepotism.
He says Mr Jamali made no secret of his absolute loyalty to President Musharraf, whom he once famously described as his "boss".
But there has been speculation that relations between the president and the prime minister deteriorated over Mr Jamali's alleged failure to fully endorse Mr Musharraf's policies.
Analysts say Mr Jamali was also the victim of a power play in the governing party.
They say his resignation will further destabilise already shaky efforts to return the country to democracy after the military coup in 1999.
Pakistan's Foreign Minister, Riaz Khokhar, meanwhile arrived in India on Saturday for talks on Kashmir with his Indian counterpart, Shashank.
It will be the first time in three years that India and Pakistan have discussed the issue and follows a series of confidence-building measures between the two nations.