The broadcast will be aired on Sunday as part of the Pride of Britain Awards.
The couple nominated nurses Jenny McGee and Luis Pitarma for the award, after they cared for Mr Johnson at St Thomas’ Hospital. They also nominated the maternity team who delivered Wilfred.
In a preview of their message, Ms Symonds said: “You continue to provide care for all of us in the very toughest of times and it’s because of you that not only is Boris still here, but that we are proud parents to our sweet baby boy.
“As a family we have so much to be thankful to the NHS for and we will never stop being grateful.”
The Prime Minister added: “Exactly right. So I want to pay thanks to the utterly brilliant team at St Thomas’ Hospital who saved my life.
“There were many of them, but I want to nominate two nurses in particular, Luis and Jenny.“
Mr Johnson was treated in intensive care for Covid-19 in the London hospital in April, before the couple’s first child together was born at University College Hospital weeks later.
Elsewhere in the show, the Duke and Duchess of Cambridge will present a special recognition award to NHS staff.
The Daily Mirror Pride of Britain Awards 2020 will be broadcast on ITV at 9pm on Sunday.