The Conservative councillor for Abbey Meads will take over the role and the robes from Derek Benfield at a ceremony in the Civic Offices this afternoon.
At 65, Coun Stoddart is younger than the 71-year-old outgoing mayor. But the retired accountant said matching Mr Benfield's energy would be a challenge.
"Derek enjoyed himself and put a lot of energy into it," said Coun Stoddart.
"He did a good job and I hope to keep it going with as much energy as he did. Most mayors get through up to 600 engagements a year, and you can easily pack in two or three a day.
"I'm reasonably fit and I'm ready for it, but I won't be doing any marathons," he joked.
Coun Stoddart, who moved to Swindon from London in 1982 and lives in Sparcells with his partner Judith, has served as a councillor on-and-off since 1982.
A former chairman of the Swindon's Conservative Association, his public service record includes spells as a governor at various schools and work with the Liden community centre.
Coun Stoddart, who has two daughters and six grandchildren, describes himself as a tradition-alist.
"I'm a bit old fashioned and more formal than most people. Perhaps I'll have to lighten up a bit," he said.
At today's mayor-making ceremony, which starts at 2.30pm, Coun Stoddart will receive the mayor's red robes and chains, and begin his new duties almost immediately by appearing tomorrow at a fete at Brook Field School in Shaw.
Mr Benfield, who stepped down as a councillor at the election, said he would be sad to see his mayoralty come to an end.
"It's been a year in my life I will always treasure and never forget," he said.
"I've been proud to be mayor of a town that is not only growing in size but in reputation for being full of good and kind hearted people."