Al-Maliki is a close ally of previous nominee Ibrahim al-Jaafari, the acting Iraqi prime minister, whose candidacy led to months of political deadlock after it was strongly opposed by Sunni and Kurdish politicians.
Humam Hammoudi, spokesman for the United Iraqi Alliance, made the announcement live on Iraqi television on Friday.
Sunni and Kurdish politicians have indicated they will not oppose Maliki's candidacy.
"If anyone is nominated except al-Jaafari, we won't put any obstacles in his way. He will receive our support," said Adnan al-Dulaimi, head of the main Sunni Arab coalition in the Iraqi parliament.
Mahmoud Othman, a leading Kurdish politician, said his bloc would not oppose Maliki.
"Maliki is clearly the front runner and there is no objection to his candidacy from any of the parliamentary blocs," he said.
The new Shia nominee is to be presented to a session of the Iraqi parliament on Saturday, when the other senior government appointments are expected to be finalised.
Leaders of the seven parties that make up the Shia alliance agreed on al-Maliki's nomination at a meeting on Friday evening, said Jalal Eddin al-Sagheer, a member of the Supreme Council for the Islamic Revolution in Iraq, the largest party in the alliance.
Six of the seven parties that make up the alliance agreed to nominate Maliki as their new candidate. The Fadhila party rejected him in favour of their own nominee, Nadim Juburi.
Al-Maliki is a leading figure in al-Jaafari's Dawa party and has often appeared as his spokesman.
Sunni and Kurdish politicians blamed al-Jaafari for the rise in sectarian tensions in Iraq and for failing to rein in Shia militia's working alongside the interior ministry.
The Shia alliance won the largest number of seats at the country's December elections but needs the support of Sunni and Kurdish politicians to form a national unity government.