The £500,000 contract for the three venues in the Cumbrian borough was awarded to Elior following a three-way procurement process.
It includes Barrow Forum Theatre, an arts and entertainment venue with a main theatre for 500, as well as a further seven events spaces with capacity from 30 to 180.
The deal also covers the Dock Museum, which has spaces including the Galleries, which opened for events for the first time in 2012.
The contract will also include the area's Park Leisure Centre, and may include occasional events at the Town Hall.
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