Salih is a former prime minister of the Kurdistan Regional Government of Iraqi Kurdistan and a former deputy prime minister of the Iraqi federal government.
Widely seen as a moderate, Salih was chosen on Tuesday after a dispute between the two main Kurdish parties delayed the vote, eventually forcing them to choose among 20 nominees.
Salih routed his main rival Fuad Hussein with 219 votes to 22.
Shia lawmaker Hamid al-Moussawi said the session was delayed because the Kurdistan Democratic Party and the Patriotic Union of Kurdistan were unable to agree on a single candidate.
The new president will have 15 days to task the nominee of the largest parliamentary bloc with forming a new government.
Under an unofficial agreement dating back to the 2003 US-led invasion, Iraq's presidency - a largely ceremonial role - is held by a Kurd, while the prime minister is Shia and the parliament speaker is Sunni.
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