The ECB said it had received an email from the man demanding a 'five-figure sum' to prevent him revealing details of a relationship that Morgan had with a woman five years ago to the British and Australian press.
Following discussions with British police, the ECB approached the man, who 'admitted and apologised for his actions, blaming jealousy'. The ECB said the man is currently in a relationship with the woman in question.
In Australia, Sydney's Daily Telegraph named the man as Nick Emery, saying he had sought Aus$65,000 in the blackmail case.
Emery told the newspaper, which splashed the 'Sexting Pomshell' story on its front page, that he was in possession of 'sexually based' messages between his partner Brooke Tsakirakis and Morgan from last year.
The workplace safety consultant said he met ECB officials in Hobart on Thursday and had withdrawn his threat.
"It's dealt with. I did the wrong thing in the wrong state of mind," Emery told the Telegraph.
"I was in a very angry and bad head space ... they were very understanding, we came to an agreement."
ECB managing director Paul Downton also said the issue had been settled.
"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," he said.
"I am pleased that this issue has now been brought to a swift conclusion. At this point we'd like to thank the Metropolitan Police for their advice, which assisted us in dealing with this in the swiftest possible manner."
England are halfway through a Tri-Series with Australia and India as they build up to the World Cup, which begins Down Under on February 14.
Morgan replaced Alastair Cook as England's one-day captain in December and scored 121 against Australia last week.
England lost that match, but bounced back to beat India by nine wickets on Tuesday. They face a second game against Australia in Hobart on Friday.
Like Sports on Facebook, follow @ETribuneSports on Twitter to stay informed and join in the conversation.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ