In a statement on Monday afternoon, Mr Jarvis, who has been the Labour MP for Barnsley Central since 2011, said he “will continue to give 110 per cent to the role” before the elections next May.
Reflecting on the “relentless pressures” of the last few years, including the pandemic, Brexit and “terrible flooding”, Mr Jarvis said he was glad to have stayed as a Member of Parliament at the same time, explaining: "I honestly don't believe we would have made the progress we have, and we certainly wouldn't have got the devolution deal over the line, if I had not stayed in Westminster. The settlement we negotiated helped take us through the worst of the pandemic and is really starting to deliver for people in South Yorkshire. ”
He said that the Sheffield City Region “need[s] someone to build on our achievements and drive us forward over the next four years,” but confirmed that it will not be him, adding: “There's still an awful lot I want to get done and I'll be working hard to get us into the best possible shape for the future. I'm letting people know my intentions now because I think it's important that potential candidates are given sufficient notice to step forward.
“South Yorkshire deserves someone of the highest calibre as their next Mayor, who can provide the leadership required.”
Speaking to The Yorkshire Post following the announcement, Mr Jarvis said he has "mixed emotions" about standing down but is proud of what has been achieved.
Despite his position, he described being a Labour mayor with a Tory government as having been "immensely frustrating" and that for now, "levelling up is just smoke and mirrors".
Labour leader Sir Keir Starmer paid tribute to the "enormous amount" Mr Jarvis achieved in the role, tweeting: "He's shown what can be done when Labour is in power, putting Labour values into action. I’m pleased that he'll continue as an MP - representing and championing the people of Barnsley."
The mayors of West Yorkshire and Greater Manchester have paid tributes, with Andy Burnham telling The Yorkshire Post he "takes his hat off" to Mr Jarvis for having held down the mayoral role at the same time as holding a seat in the Commons.
Mr Burnham went on: Obviously it is a disappointment in some ways but there is an opportunity now for someone else to come in and pick up the reigns.
"We will miss him but I think devolution is now established in the North of England and our voice is getting stronger."
Tracy Brabin said that she will "miss" Mr Jarvis in the role, but added: " I'm hoping that the new mayor whoever that will be will be really happy to work with me as we look to the future and really make a big case for Yorkshire as a brand."
The Labour MP for Barnsley Central was elected to the mayoral role in 2018 when it was created, beating Conservative candidate Ian Walker in two rounds of voting.