Rival political forces in Iraq have failed to form a government since early parliamentary elections were conducted in October 2021.
On Thursday, Rashid, a consensus candidate backed by the Kurdistan Democratic Party (KDP), was picked to be Iraq's head of state in a vote at the 329-strong parliament.
Rashid gained 162 votes out of 269, beating out his rival, incumbent Barham Salih of the Patriotic Union of Kurdistan (PUK) party, the legislature's media department said.
In the first round, neither Rashid nor Salih secured the required two-thirds of votes.
Rashid, 78, served as a minister of water resources in Iraq for seven years starting from 2003.
The parliament had previously failed three times to pick a head of state earlier this year.
By custom, a Kurdish politician serves as Iraq's president.
The post of parliament Speaker is traditionally occupied by a Sunni Muslim, and the prime minister is a Shi'ite.
Rashid was sworn in at parliament and shortly afterwards, he tasked Mohammed Shia al-Sudani with forming a new cabinet.
Al-Sudani has been nominated for the prime minister post by the Iran-backed Coordination Framework political alliance.
In August, violence erupted when loyalists of populist Shi'ite cleric Moqtada al-Sadr stormed government buildings to protest al-Sudani's nomination.
Al-Sadr rejected al-Sudani's nomination and has been calling for the dissolution of parliament and pushing for new elections.
In the run-up to Thursday's vote, nine rockets landed in the fortified Green Zone in Baghdad and its vicinity, injuring three people, the military-linked Security Media Cell reported.
So far, there has been no claim of responsibility.
The Green Zone houses the parliament, government buildings and foreign embassies.
