According to the ECB, an Australian man had demanded a five-figure sum to prevent a story about one-day skipper Morgan and a previous girlfriend appearing in national newspapers in Australia and Britain.
"The allegations related to a brief relationship Eoin had with a woman from Australia five years ago," a statement said.
"Following liaison with the Metropolitan Police, our support team on the ground in Australia investigated the blackmail.
"This involved approaching the man in question who, when confronted, admitted and apologised for his actions, blaming jealousy."
The man involved is understood to be in a relationship with the woman Morgan once dated.
The ECB said they would not seek to press charges.
"We will not allow anyone to disrupt our team's preparation or performance in the tri-series and as we build up to the World Cup. I am pleased that this issue has now been brought to a swift conclusion," Paul Downton, the ECB's managing director, said.
Morgan was named as England's one-day captain after Alastair Cook was removed from the post in December.
(Reporting by Martyn Hermanm editing by Pritha Sarkar)
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