The budget retailer would be the final stage of a 15-year development which includes the neighbouring Tesco supermarket and housing estates.
The 14,000 square foot store will be built on land off Peter Chambers Way.
Developer Lindum Group said B&M had been hoping to bring a shop to the town for a long time.
Development planner Robert Jays told East Lindsey District Council’s planning committee: “We have been involved in the area for 15 years, and this is the last piece of development land. The Tesco is now operational and the nearby care home is under way.
“Mablethorpe has been a long-term target for the client, and the store will be valuable given the cost of living crisis.
“It will raise the profile of the town and improve retail offering, while contributing to investment.”
Around 40 new jobs will be created as a result.
The company said it had worked to accommodate concerns from residents. The proposed height of the building was reduced by two metres so it would not overshadow neighbouring properties.
They claimed the vast majority of people who took part in a consultation backed the plans, and were happy they wouldn’t have to travel to shops out of town.
Coun Helen Matthews raised the question of whether the developer would be investing in the local community.
“I’m very familiar with this area. It’s great we’re putting a supermarket here. But could we require something like a play area, litter picking or community improvements? It’s a very run-down area,” she said.
Council officers said it was too late in the process to require the Lindum Group to do this, but the firm could be encouraged to give back to the community.
The plans were passed unanimously.