Ms Jones secured 25,364 votes to see off the challenge of current mayor Peter Davies, standing as an independent, in a tight contest.
The result was decided on a count of second preferences after just 590 votes separated them on first preferences.
Ms Jones, who has been the councillor for Askern Spa ward for the past seven years, will become the town's first female and second Labour mayor.
Incumbent mayor Mr Davies came second after receiving 24,725 votes.
He stood as an independent candidate after quitting the English Democrat party in February over claims of an influx of new members joining from the British National Party.
The turnout for the vote was 28%, with 62,132 voting out of an electorate of 223,608.  In 2009 the turnout was 39%.
Ms Jones said her win was a "hugely proud and humbling moment".
She said: "Doncaster's spoken and it has said it wants a mayor who will always be on its side, who will stand up against any cuts that's Tory led, will go out and sell Doncaster to the world, to bring jobs and growth here, that's what we need.
"The people of Doncaster have put great responsibility on my shoulders. I accept it and say I will work my socks off for you."
Mr Davies congratulated Ms Jones on her "somewhat narrow victory".
He said: "I have enjoyed every minute of the experience, I have been privileged to service the people of Doncaster with what I think has been four years of common sense and taking nonsense out of council and political life."
He added: "I will not miss the council meetings, which are horrendous in the extreme more often than not."
All three main political parties were represented in the election alongside the English Democrats, Trade Unionists and Socialists, and National Front.
Three independent candidates also stood as well as a Save Your Services representative.
Ms Jones and Mr Davies were the only candidates remaining after the first round.
Labour's Ros Jones has won the race to become Doncaster's elected mayor.