The 45-year-old comedian, who has lived in the UK with his wife for many years, shared a video of himself on Twitter outside the hospital with workers.
This month's strikes are the first mass walkouts in the 106-year history of the Royal College of Nursing, with NHS staff voting to strike over years of below-inflation pay rises and adverse working conditions.
Delaney wrote: "Gorgeous day for a nurses’ strike outside Great Ormond St Hospital. So grateful for their unmatched care & skill.
"Now let’s get them the f***ing pay rise they deserve & that the nation can *easily* afford. Austerity is a choice so change your mind or get in the bin!"
This is not the first time that Delaney — a long-time Labour supporter — has shown solidarity with striking workers this year.
In July, he was pictured alongside RMT boss Mick Lynch on a picket line at King's Cross Station as a part of the ongoing industrial action in the rail industry.
Delaney has spoken of his left-wing political views frequently, offering public backing to figures including Jeremy Corbyn in the UK and Bernie Sanders in the States.
Delaney is best known in the UK for his work alongside Sharon Horgan in the sitcom Catastrophe, in which he plays an American who moves to Britain after a woman he met there becomes pregnant.
It ran for four seasons, concluding in 2019, and earned Delaney an Emmy nomination for his writing work.
More recently, Delaney played one of the villains in the reboot of the Home Alone franchise for Disney+, entitled Home Sweet Home Alone.
Next year, he's due to make an appearance alongside Tom Cruise in the action spectacular Mission: Impossible – Dead Reckoning Part One.
Watch: Rob Delaney says being a parent made him funnier