Worth £1.9m, the contract will see Elior operate three Illy café bars, two public bars, a restaurant and vending services within the 529-seat theatre complex, separate Dock Museum and Park Leisure site.
Keith Johnson, assistant director of community services at Barrow Borough Council, said: "The Elior team built their response to the tender around our brand rather than imposing their own identity on us.
"Their reputation and experience in concession and event catering gave us confidence in their ability to deliver. They particularly impressed us by mobilising the contract, just three weeks after signing the deal."
Angela Urwin, Elior operations manager, added: "We have already received excellent customer feedback regarding the Illy Café concept bars, the fresh on-site bakery and new streamlined menu.
"We are keen to be proactive and creative in our approach to event catering at the Forum and have already arranged a bespoke Scottish theme menu, which includes a piper and whisky tasting for the upcoming Proclaimers concert in September."