Thousands of voters lined up outside polling stations to cast their ballots when voting started from 0200 GMT.
"It was a special day for me," said Hassan Suleyman, who cast his ballot in the port town of Bossaso on the Gulf of Aden.
The May 25 balloting are the first one-person one-vote elections since 1969 when Somali dictator Siad Barre seized power.
"Today is a priceless historic day," electoral council chairman Abdirisak Ahmed said. "Many people believed the victory we have secured today was impossible."
Another voter, Warsame Mohamed, said "people are happy" despite the long wait.
The United Nations, African Union and a number of world governments hailed the Puntland process as "historic."
"The partners believe that Puntland's experience with direct elections has the potential to inform and inspire the expansion of democracy across Somalia, at all levels of government," they said in a statement.
Polling was however postponed in three out of the region's 33 districts, including state capital Garowe, the Transitional Puntland Electoral Commission said in a statement Wednesday, referring to unspecified security incidents.
An analysis published by the U.N.'s humanitarian agency OCHA this month said the transition to the new electoral system in Puntland had been "volatile and fraught with obstacles."
Puntland, an arid oil-rich region in northeastern Somalia, declared autonomy in 1998 and relations with the central government in Mogadishu have often been tense.
Somalia's President Hassan Sheikh Mohamud, who was elected by lawmakers a year ago, announced in March that the next national elections would be by universal suffrage.
Currently, voting follows a complex indirect model where state legislatures and clan delegates pick lawmakers for the national parliament, who in turn choose the president.
The Puntland local elections are being held ahead of a regional parliamentary poll due in January 2024.
Seven parties are running on Thursday, but some opposition politicians have already expressed concerns over the process and accused state president Said Abdullahi Deni of manipulating the election procedure.
Deni's term is due to end in January and the opposition has warned he may be seeking to change Puntland's constitution to enable him to extend his mandate.
A Puntland opposition forum that met in mid-May said it "protests any attempt to open a review process for the constitution at this stage of the transition period when the mandate is close to expiring for both parliament and the government."
"This can be an attempt to seek unlawful mandate extension," the forum said in a statement.
More than 387,000 voters have been registered for the Puntland elections, the majority aged between 18 and 30. They and are choosing from among 3,775 candidates, 28 percent of them women, the TPEC said.
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