Sound engineer Tobius Gough, from Longfield, Kent, appeared on screen wearing a tight t-shirt to test the equipment before Mrs May's tearful announcement.
He quickly became a social media hit with users saying: “Hot Podium Guy for PM” and “He looks strong and stable.
Twitter user Jesse Harber wrote: "Presenting the new PM" accompanied by a picture of Mr Gough at the podium.
Chris Mandle also said: "Using Game of Thrones succession logic, I'd like to suggest Hot Podium Guy as the new Prime Minister.'
"Prodium guy so far the only person to do his job efficiently at Downing Street in the last three years," tweeted Laura Holland.
Sam Fishwick also asked: “Who is this absolute unit?" whilst another tweeter said: "The guy setting up the podium was well hot."
The guy setting up the podium was well hot— the brookie monster (@bgirlrhapsody)24 May 2019
The engineer's appearance came ahead of Theresa May’s speach outside Number 10 where she announced her resignation as prime minister.
Mrs May said she will resign as Tory leader on 7 June, two days after President Donald Trump ends his state visit to the UK.
In an emotional statement in Downing Street, Mrs May said it was in the “best interests of the country” for a new prime minister to lead efforts to deliver Brexit.
if there was an immediate PM vote how many people would choose the guy setting up this podium over Boris https://t.co/xWy9JPRwWw— karl polanyeet (@said_mitch)24 May 2019
Her voice cracked as she said: “I will shortly leave the job that it has been the honour of my life to hold - the second female Prime Minister but certainly not the last.
“I do so with no ill will, but with enormous and enduring gratitude to have had the opportunity to serve the country I love.”