Campbell Ritchie was also voted in unanimously as Cllr Exton's deputy.
They will don their official regalia at the formal robing ceremony on May 28 at a public ceremony in the town hall.
Speaking about her appointment, grandmother of four Cllr Exton thanked the community for its vote of confidence in her.
She said: “Thank you for all your messages and kind words. I was totally overwhelmed, you are always there for me, that means a lot.
“I am looking forward to the next year ahead, representing the council, residents and this beautiful town of ours, I will do everything I can to support the town and residents.
“With you all beside me, we can do this,” she said.
Town councillor Gavin Grant, who is also the Wiltshire councillor, said: “I was delighted to nominate Julie Exton as Malmesbury’s next mayor and to see Julie elected unanimously by my town councillor colleagues.
“We have had a brilliant mayor in Fran Vandelli who received a very well deserved ovation from us all.
“I believe Julie is set to be another outstanding mayor.
“She has worked hard as deputy mayor, been an excellent town councillor and has strong connections with parts of our community that are not as familiar with what our town council does and how it works.
“Julie will help change that," he said.
“I also believe she will get great support from our new deputy mayor, Campbell Ritchie.
“I work closely with Campbell on the town team and in our campaign to rid Malmesbury of the pollution of single use plastics. He will do a terrific job as deputy mayor.”
Cllr Exton will be in the role for a year with husband Phil as consort.