In a vote by secret ballot, Adeang received 10 votes and while Delvin Thoma had eight votes.
The vote for a new president follows the successful vote of no confidence last week in the administration of Kun, who assumed office in September 2022.
Adeang is the longest serving MP in the current parliament, having launched his political career when he first stood in the 2001 general elections.
He also served as the Speaker of Parliament in 2004 and 2008 and held a number of cabinet portfolios including minister assisting the president as well as finance and justice, the Nauru government said in the statement.
He was a long-time finance minister in Nauru and along with former president, Baron Waqa, was accused of receiving kickbacks from a phosphate exporting company.
They have both denied they were involved and although an Australian Federal Police investigation into the event was launched in 2015.
The Refugee Action Coalition's Ian Rintoul told RNZ Pacific that Adeang, was his "preferred choice" of the candidates.
He said unlike other Nauru presidents, whom he has described as "ruthless and corrupt", Adeang was someone who was a little more sympathetic to the refugee situation.
"I would be hoping that he would be taking a much more ciritcal view of [the Australian government] using Nauru as a detention centre than the previous president."
However, Rintoul added "I don't really hold any hope that he's about to close down the tension on the room anytime soon."
In 2016, Adeang said he understood a lack of long-term solutions was distressing for refugees on Nauru.