Councillor Paul Smith was voted in as Campbell’s deputy mayor.
Campbell said: "I would like to thank my colleagues for their support.
"It is a great honour to be elected as mayor of Malmesbury and I am looking forward to representing our fantastic town to the best of my ability.
"I feel very lucky to have become mayor of a town with so much history, sense of identity and strength of character.
"I would like to pay tribute to our retiring mayor, Julie Exton. She has led by example and packed so much into her mayoral year.
"She received a well-deserved and sustained ovation at our virtual council meeting last night.
"The year ahead has challenges as the Covid-19 emergency continues.
"I am proud of the response Malmesbury Town Council and staff team has made to establish a partnership with local charity HEALS and, with 100 registered volunteers, ensure all residents can access food, essential supplies, prescriptions and other vital support.
"We expect this will continue for some months to come.
"We also have to ensure that Malmesbury recovers from this emergency as strongly as possible and we will continue working hand in hand with Malmesbury Town Team to give support to our brilliant local businesses and high street.
"In addition, the usual work of the town council continues, such as the progress of our Neighbourhood Plan and running town council services well, which will include getting our parks and town hall open again when permitted.
"We also need to have opportunities for fun as a town in the year ahead.
"We might have to be physically distant for a while but this shouldn’t mean becoming socially remote or losing our connections to one another.
"Malmesbury Town Council is organising its community events to be virtual and as participative and entertaining as possible, and we will support other community groups organising events and activities.
"I would also like to congratulate Paul Smith on becoming deputy mayor. Paul has great experience and enthusiasm and will do a terrific job."