Han said in a televised briefing he determined he would quit to take "a bigger responsibility" for the country. South Korean media reported Han will officially launch his presidential campaign on Friday.
Han was appointed prime minister, the country's number two post, by then-president Yoon Suk Yeol, who was removed from office, triggering the by-election.
Finance Minister Choi Sang-mok is seen standing in as acting president as required by law.
The main conservative People Power Party remains in disarray over Yoon's imposition of martial law in December.
Observers say Han is expected to align with the People Power Party to launch a unified conservative campaign against liberal front-runner Lee Jae-myung.
Han, 75, is a career bureaucrat with about 40 years of public service and a Harvard doctorate in economics. He has held top posts under both conservative and liberal governments, including trade minister, finance minister and ambassador to the US.
He's served as prime minster twice, first under liberal president Roh Moo-hyun from 2007-2008 and later under Yoon.
Han's supporters say his extensive government experience, especially on economic affairs, would make him a right leader who can deal with US President Donald Trump's aggressive tariff policies and other economic problems.
But his critics say Han - who has never had an elected post - has no strong political support base, is too old to become president and lacks a tough leadership to tackle contentious issues.
with AP
7°C