Mr Dubke tendered his resignation on 18 May and is leaving on good terms, according to Axios News, a politics website which first reported his exit.
White House Chief of Staff Reince Priebus said Mr Dubke had agreed to stay on until Mr Trump returned from his trip to the Middle East and Europe on Saturday.
"Mike tendered his resignation just before the President's historic international trip and offered to remain onboard until a transition is concluded," said Mr Priebus.
"Mike will assist with the transition and be a strong advocate for the President and the President's policies moving forward."
According to news website Politico, Mr Dubke, 47, provided few details on his departure in an email to friends.
"The reasons for my departure are personal," he wrote, "but it has been my great honor to serve President Trump and this administration.
"It has also been my distinct pleasure to work side-by-side, day-by-day with the staff of the communications and press departments.
"This White House is filled with some of the finest and hardest working men and women in the American Government."
Analysis - BBC North America Reporter Anthony Zurcher
Mike Dubke was an outsider hired to bring focus and discipline to the Trump White House communications operation. After just three months on the job, he's back on the outside again.
In the vast scheme of things, whether Dubke willingly quit or was forced to resign isn't all that important. Despite his title, it's difficult to gauge how much influence he ever had with the president.
What's worth noting is that the first change in what could be a larger White House shake-up has come in the communications department, with rumours of further reorganisation imminent.
This lends credence to earlier reports that the president views his administration's ongoing difficulties as a messaging problem, and not one of policies or management.
If that's the case, it appears the new message will be delivered with bare knuckles.
Old campaign hands, like the pugnacious Corey Lewandowski, are being considered for White House jobs and the president could be hitting the road for more unscripted big-venue rallies with his supporters.
It would mark a return to the campaign tactics that won Mr Trump the presidency - where every stumble or controversy was countered aggressively, political decorum and tradition be damned.
President Trump is reported to have been frustrated with White House messaging amid congressional and FBI investigations into whether his campaign officials colluded with an alleged Kremlin plot to help him win the presidency.
He recently raised the idea of scrapping the daily news briefing altogether and holding one himself every fortnight.
According to Axios, Mr Trump plans to follow through on that plan by taking more questions directly from the media.
Press Secretary Sean Spicer - who is expected back at the media podium on Tuesday - will reportedly hold fewer on-camera briefings.