His withdrawal followed inconclusive April 17 elections that led his party to choose foreign minister Jeremiah Manele as its parliamentary leader -- in effect its candidate for the premiership.
Solomon Islands MPs will choose a new prime minister in a secret ballot on Thursday.
During four spasmodic spells as the Pacific nation's leader, the 69-year-old Sogavare has manoeuvred through armed coups, riots and the rise of China.
Sogavare said he wanted to thank the people for the "privilege and honour" of serving his country.
But he took a parting shot at his critics, saying his family and children had been subjected to "unprecedented verbal abuse".
"I've been accused of many things. But not a single one of these accusations have been proven," Sogavare told a news conference.
"I have been continuously vilified in the media," he said. "But that did not waver my resolve. It has not been easy."
His latest term in office began in 2019, when he abruptly switched diplomatic relations from Taiwan to China, unleashing a wave of investment and aid from Beijing.
Sogavare signed a security pact with Beijing in 2022, and has overseen the rapid expansion of Chinese interests across the archipelago, ringing alarm bells in Western capitals.
In the April 17 poll, the prime minister only retained his seat by a narrow margin and his party fell short of an outright majority.
But Sogavare's withdrawal from the leadership does not necessarily spell the end of his party's embrace of China.
As foreign minister, it was Manele who travelled to Beijing in 2019 to formalise diplomatic relations.
- Teetotal black belt -
Manele was a career diplomat before entering politics in 2014, according to a biography posted by the World Trade Organisation, and he previously served at the United Nations in New York.
He has in the past lauded China for its generous aid and infrastructure funding, and has stressed Solomon Islands' firm commitment to relations with Beijing.
Sogavare said he was confident his Ownership Unity and Responsibility Party had secured enough support from coalition partners to give it a slim majority of 28 MPs in the new 50-seat parliament.
Nominations for the top job will close Tuesday afternoon, Governor General David Vunagi said in a written notice on Monday.
Rival parties have expressed a desire to wind back China's influence if they form a government.
Four opposition parties have reportedly banded together to fight for power, with the three-party CARE coalition linking up with the Solomon Islands United Party.
With a combined 20 seats, according to provisional results, they would have to recruit more MPs for a chance to govern.
Sogavare's departure marks the end of a tumultuous period in office but it is hard to rule out a return in the future.
The teetotal black belt in karate was born to missionary parents within the Seventh-day Adventist church, and his faith is a defining part of his public persona in the deeply Christian nation.
In his rags-to-riches origin story, Sogavare claims he rose from being a humble toilet cleaner in the country's public service to become the powerful Commissioner of Inland Revenue before entering politics.
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