Morgan has said that he had been receiving messages saying that he was a "marked man" and it was a "promise" that he was "getting killed". The TV star's son Spencer aged 28 was also receiving abusive trolls, saying that he would "get it" if his father did not.
A man has since been arrested on suspicion of making threats to kill.
Speaking to the Sun newspaper, Piers Morgan said, "People think it’s perfectly OK to make death threats to public figures on social media but it’s not - there has to be a line drawn, especially when family members are targeted".
"That’s why I reported it and I am grateful to the Met Police and Greater Manchester Police for taking it so seriously".
He tweeted, "Cowardly threats have consequences".
"On Wednesday, 17 February 2021, police received a report of malicious communications relating to messages sent on social media", the Metropolitan Police said in a statement.
"Officers have spoken with the complainant in person".
"On 3 August a 43-year-old man was arrested in Manchester on suspicion of making threats to kill. He has been released under investigation while inquiries continue".
"The investigation remains ongoing".