The resignation of Hailemariam, in power since 2012, comes amid protracted anti-government protests and follows a nationwide state of emergency last year.
His stepping down from power is unprecedented in the vast East African country.
The letter was accepted by the executive committee of Hailemariams party, the Southern Ethiopian Peoples Democratic Movement (SEPDM), as well as the wider ruling coalition, The Ethiopian Peoples Revolutionary Democratic Front (EPRDF), state-backed media said.
His resignation will be confirmed once the full EPRDF council meets.
In a short statement, Hailemariam said he was not quitting politics, but wanted to continue his work to reform Ethiopia.
"My decision is to be part of the ongoing reform programmes," he said, according to Fana.
Hailemariam oversaw a smooth handover on the death of former Marxist rebel Meles Zenawi, turning the relatively little-known politician and technocrat to an influential leader.
However, in 2015, months of anti-government demonstrations spread across Ethiopia, leaving hundreds dead and prompting parliament to declare a 10-month state nationwide state of emergency in October 2016.
The emergency quelled the worst of the violence but periodic uprisings still occur.
This week disenchanted young men wielding sticks and rocks meanwhile blocked roads and businesses stayed shuttered in and around the capital Addis Ababa.
In a bid to ease tensions, the government last month began issuing a string of pardons and prisoner releases, after Hailemariam said jailed "politicians" would be released "to improve the national consensus and widen the democratic platform".
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