The men were shot or hanged on Tuesday after appeals were exhausted, officials from Gaza’s de facto rulers, the Islamist Hamas movement, said.
Hamas did not seek the approval of Palestinian President Mahmoud Abbas, as required under Palestinian law.
It underscores the continuing divisions between the main Palestinian factions.
Hamas and President Abbas’ Fatah party signed a unity deal in 2014 designed to end a seven-year split which saw the West Bank and the Gaza Strip governed by rival administrations.
However, the agreement has never been properly implemented, leaving Hamas still effectively in charge of the coastal territory.
The three men, one of whom was reportedly a policeman employed by the West Bank-based Palestinian Authority, were executed at dawn.
The general prosecutor’s office in Gaza said the men had been put to death “to achieve public deterrence and block crime”.
A Gaza security source told the BBC the execution had been attended by the families of the murder victims, the attorney general and representatives of Palestinian factions.
Human rights groups and the UN had called on Hamas not to carry out the sentences.
The step marks a resumption of judicial executions for the first time since the 2014 reconciliation pact.
Palestinian Authority attorney general Ahmed Brak told Reuters news agency that “carrying out the executions represents a flagrant violation of the Palestinian basic law”, according to which the president must ratify death sentences.
Those who were involved in Tuesday’s executions were complicit in murder and would be held accountable, he said.
According to Human Rights Watch, more than 40 people have been put to death in Gaza since 2007, including 23 suspected collaborators during the 2014 war with Israel.
Most of those executed were convicted in military courts or executed summarily, without a judicial ruling, it said.