The union will be led by Fatah affiliates for the first time in 12 years, but Hamas is claiming its party members were the real winners, the newspaper said.
Although most Unrwa employees voted for Hamas-affiliated candidates, Fatah affiliates will lead the union because of a special representation system, which carves up the electorate into three unequally-sized constituencies, Haaretz said.
Although the candidates' political affiliations were known to the voters, the candidates are not officially aligned with any party, as this would conflict with Unrwa regulations on impartiality.
John Ging, Unrwa's director of operations, said that those elected stand to lose their jobs unless they disassociate themselves from political parties.
In a letter, he said he would address the elected candidates about this "worrisome situation", and that his decision on their future employment would be "dependent" on their reaction, Haaretz
Ging said employees must not "be under the influence of any political party in the conduct of their work".
Hamas, which some believe has lost popular support after Israel's 22-day offensive on Gaza, has been especially vocal in declaring victory in the union election.
The organisation's media stated that 63 per cent of all voters voted for Hamas candidates, who won 17 out of the 27 board seats in the three sectors.
Fatah supporters, meanwhile, announced that their comrades had won five out of nine seats in the trade union's executive council, giving them the power to appoint the chairman, deputy chairman and secretary, Haaretz said.
During his three years in Gaza, Ging has taken steps to limit political involvement by Unrwa employees.
He sought to end political propaganda within schools, and to bar employees from making political or bellicose statements to the media.
Ging's letter, which Haaretz said he sent to a small group of employees, noted that parties "hostile" to Unrwa have over the past few years advertised the victory of various political candidates within internal Unrwa elections.
But he wrote that the 2009 election was the first time that such declarations came from people inside the Strip, giving their statements added credibility, according to Haaretz.
About 10,000 people took part in the election, including 7,000 educational workers, 2,000 heath and administrative workers and 1,000 manual labourers.