The Christmas Eve vote followed the resignation earlier this month of Siaosi Sovaleni who quit just ahead of a no-confidence motion by lawmakers.
Eke assumes office less than a year before the South Pacific island nation of 105,000 people is to hold its next election.
A former finance minister, Eke won the secret ballot by 16-8 votes, defeating the only other candidate, Trade Minister Viliame Latu.
They both addressed parliament for about 20 minutes before the results were announced on Tuesday afternoon.
The tourism-dependent Tonga has struggled to rebound from the impact of the coronavirus pandemic, growing threats from climate change and a catastrophic 2022 volcanic eruption and tsunami, which battered beachfront resorts, homes and businesses around the country's 171 islands.
Tonga's parliament consists of 17 lawmakers elected by the public and nine who are nobles, elected by a group of hereditary chiefs. Two members of parliament were unable to vote.
The resignation of Sovaleni capped a period of fraught relations between his government and Tonga's king.
Eke will be officially sworn in at the next parliament session in February.
He emerged on Tonga's political scene in 2010 and held several profile positions before losing his seat in 2017.
As finance minister, he spent time at the World Bank in Washington working on financial reform programs for Tonga.
He returned to parliament in 2021 and was in the running to be prime minister but lost out to Sovaleni.
Sovaleni's tenure was rocked by occasional tensions between Tonga's monarchy and elected lawmakers in a fledgling democracy after reforms that transferred powers from the royal family and nobles to regular citizens in 2010.
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