Muscat stated he would resign after his successor is chosen by January 12.
He was first elected prime minister in 2013 and said he will stay in office until his Labour Party has chosen a successor in a process starting January 12.
Led by Dutch MEP Sophie in't Veld, it will examine doubts about the Judiciary's independence and investigate allegations of high-level corruption.
"As prime minister, I promised two years ago that justice would be done in the case of the murder of Daphne Caruana Galizia", Muscat said.
Findings from the probe resulted in charges against Yorgen Fenech, a 38-year-old businessman with links to high-ranking officials and ministers.
"Our country thus will start a short process of approximately a month for the Labour Party to choose a new leader and a new prime minister", he added.
Her murder triggered outrage in Malta, and angry protesters repeatedly took to the streets last week demanding that Muscat immediately resign for failing to clean up politics in the country.
Mr Schembri, who had previously been named in the Panama Papers, quit.
Fenech is the owner of 17 Black, a company based in Dubai that was allegedly set up to transfer money to the Panamanian companies - Hearnville Inc and Tillgate Inc - owned by former energy minister Konrad Mizzi and Muscat's ex chief of staff Schembri.
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Investigations into Caruana Galizia's murder intensified when Mr Theuma was pardoned on Monday.
The meeting came a day after the main suspect in the 2017 vehicle bomb killing, tycoon Yorgen Fenech, was charged with complicity in the murder and had his assets frozen by a court. "The situation is desperate", she had written referring to what she unearthed with her digging into suspected widespread corruption in Malta's political and business circles. Despite having a reputation for taking action against party members who fell out of line, Mr Muscat failed to take serious action - Mr Mizzi was made a minister without portfolio and Mr Schembri was kept in place.
Although Schembri, Muscat's former chief of staff, was arrested Tuesday, his release on Thursday sparked accusations of a cover-up.
Again, the prime minister did not act against his colleagues.
In his address, the prime minister struck a defiant tone, saying that every day since the murder he had shouldered responsibilities in "the interests of the conclusion of the case".
But the slain reporter's family contended Muscat's departure won't satisfy those in the nation who are determined that corruption and cronyism between politicians and business figures be rooted out.
Vincent Muscat later told police the bomb had been placed in Caruana Galizia's auto while it was parked outside the walled compound where she lived.
The three have pleaded not guilty and are still awaiting trial.