Abela, 42, will replace Joseph Muscat, who is stepping down midway through his second term as prime minister amid demands for accountability over the 2017 murder of an anti-corruption journalist.
Muscat tweeted his congratulations, saying, "Proud to be handing over to him #Malta PM office on Monday," when Abela will be sworn in.
Abela was scheduled to address the party Sunday afternoon. Labour has a comfortable majority in Parliament.
Before being chosen as Labour leader, Abela said he would work to restore Malta's reputation for rule of law. European Union lawmakers had criticized the member nation's judiciary and police.
A close aide to Muscat was questioned in connection with journalist Daphne Caruana Galizia's murder, denied wrongdoing and was released while still under investigation. A Maltese hotelier, who denies involvement, has been accused of complicity in the killing. Three other men, accused of triggering the car bomb, are under arrest.
Muscat had beaten Abela's father in the race for the party leadership in 2008. George Abela was later appointed president, serving from 2009 until 2014.