His wife, Tracey Kurland, gave birth on Thursday. The couple announced they were expecting a child in April.
Mr Engelson took to Instagram to express his delight at the news.
He wrote: “So proud to introduce Ford Grace Engelson to the world!
“Turns out 2020 ain’t so bad after all!
“My wife is a beautiful champion… I’m officially the happiest guy I know.”
The caption accompanied a picture of the happy parents cradling their baby.
Meghan married Mr Engelson, a film producer, in 2011.
The couple were together for seven years before getting married.
However just two years after their Jamaican wedding the couple were divorced.
READ MORE: Prince Charles kept special memento from Meghan and Harry’s wedding
Meghan went on to marry Prince Harry in May 2018 in an event watched by hundreds of millions around the world.
The couple welcomed their own child, Archie Mountbatten-Windsor, one year later.
However in January of this year Harry and Meghan caused a sensation by announcing they were stepping down as senior members of the royal family.
Instead the couple said they would become “financially independent” and split their time between Britain and North America.
After a brief spell in Canada the couple moved to California shortly before the state was put into coronavirus lockdown.
During a charity dinner hosted by Sentebale Prince Harry revealed how much thought he’d given the decision to step back.
He said: “The decision that I have made for my wife and I to step back is not one I made lightly…there really was no other option.
“I have accepted this, knowing that it doesn’t change who I am or how committed I am.
“But I hope that helps you understand what it had to come to, that I would step my family back from all I have ever known, to take a step forward into what I hope can be a more peaceful life.”
Meghan and Harry recently moved to a new £11.2m situated to the north of Los Angeles.