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.
"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 currently halfway through a Tri-Series with Australia and India as they build up to the World Cup, which begins on February 14.
Morgan replaced Alastair Cook as England's one-day captain in December and scored 121 against Australia last week.