The city's mayor previously said he would offer dinner to anyone who could locate the duo for making a "mockery" of his city.
Two foreign tourists who sped down Venice's Grand Canal on motorised surfboards were fined on Wednesday, after a hunt by city authorities.
The young men were filmed zig-zagging around gondolas and waterbuses through Venice's main thoroughfare, prompting the city's mayor to call for the pair to be punished.
In a statement, the mayor’s office said the duo were fined 1,500 euros ($1,530) each, after the footage sparked outrage when it was posted online.
Posting a video of the surfers on social media, Venice Mayor Luigi Brugnaro asked people to help apprehend “two overbearing imbeciles who are making a mockery of the city.”
He even promised dinner for anyone who identified the surfers.
Surfing, canoeing and paddle boarding are prohibited on Venice's Grand Canal, one of the Italian city's major water traffic highways.
The pair also had their boards confiscated by the authorities, Brugnaro later tweeted on Wednesday afternoon, without indicating if he had in fact invited anyone to dinner.
“Shameful,” commented one Instagram user on a clip of the incident shared online. “They need to be expelled from Venice for life, mamma mia.”
But some others on the social media platform approved of the surfers, saying they thought it would be "great" and more cost-effective if everyone could travel around Venice in this way.
Venice, which attracts 20 million visitors each year, has long suffered from over-tourism.
It has a long list of rules governing the behaviour of visitors, who some residents feel can be a nuisance, especially during peak seasons.
In 2019, the city fined two German travellers $1,000 for making coffee on the 430-year-old Rialto Bridge.
Visitors also are prohibited from swimming in the canals and from eating on the steps of monuments, which can land them with large fines.
As of next year, day-trippers will have to pay a visitor’s tax to help offset the elevated costs of providing services in the canal city.