England had threatened to call off their tour unless a "significant number" of the 13 blocked media, including the BBC, were allowed in.
The Zimbabwen government said it had lifted the ban and blamed the delay on insufficient information being provided by the journalists.
England were now set to fly to Harare for the scheduled start on Friday.
"The whole incident is regrettable but it has been resolved," Morgan said in a statement.
A Zimbabwe government spokesman had said in a statement that the media ban was directed at those who had been consistently hostile to the Zimbabwean authorities.
But, following the ECB's threat to cancel the tour if the ban was not lifted, Robert Mugabe's regime performed an about turn.
