Governor-General Sir David Vunagi announced outside parliament on Thursday that Manele had won 31 votes, to Opposition leader Matthew Wales' 18.
Police boosted security in the capital Honiara as newly elected lawmakers arrived at parliament on Thursday to vote.
The election was the Solomon Islands' first since the government switched diplomatic allegiances. (AP PHOTO)
A national election in April failed to deliver a majority to any political party, and two camps lobbied to win support from independents ahead of the vote for prime minister.
The election is being closely watched by China, the United States and Australia because of the potential impact on regional security, after incumbent Prime Minister Manasseh Sogavare struck a security pact with China in 2022.
Australian Prime Minister Anthony Albanese said he looked forward to working closely with Manele. "Australia and Solomon Islands are close friends and our futures are connected," he wrote on X.
Sogavare, who built close ties with Beijing during five years in power, did not seek re-election to the top political office and his party backed Manele.
Manele said outside parliament on Thursday "the people have spoken", and called for calm.
"Today we show the world we are better than that - we must respect the democratic process for electing our prime minister," he said.
The economy was slowly recovering from the COVID-19 pandemic and 2021 anti-government riots, and the government would soon unveil tax, forestry and minerals policies, he added.
Manele is a former diplomat who entered parliament in 2014, and travelled to China as foreign minister in 2019 to formalise Solomon Islands' switch in diplomatic ties from Taiwan to Beijing.
On Monday, Manele said he would keep the "same foreign policy basis - friends to all and enemies to none".
Lowy Institute research fellow Mihai Sora, a former Australian diplomat in the Solomon Islands, said Manele has "a strong track record of working well with all international partners", compared to Sogavare who was "a polarising figure".
Australian National University's Pacific expert Graeme Smith said Manele was capable and "a big change in style" for the Solomon Islands.
Congratulations to Jeremiah Manele on his election as Prime Minister of Solomon Islands. I look forward to working closely with him. Australia and Solomon Islands are close friends and our futures are connected. 🇦🇺🇸🇧— Anthony Albanese (@AlboMP) May 2, 2024
Manele's OUR party, which has pledged to build more infrastructure, won 15 seats, and gained four seats under a renewed coalition with two micro parties. It needed support from independents to reach a majority in the 50-seat parliament. A total of 49 votes were cast with one lawmaker absent.
Wale said on Wednesday that lobbying of politicians ahead of the vote was dominated by "people asking for money and positions".
The government had failed to create jobs and the economy was dominated by logging and mining companies which shipped resources to China, while health clinics were unable to obtain medications such as paracetamol, he said at a Solomon Islands National University event.
20°C