Southwest Airlines will begin charging customers a fee to check bags, abandoning a decades-long practice that executives had described last fall as key to differentiating the budget carrier from its rivals.

Southwest, which built years of advertising campaigns around its policy of letting passengers check up to two bags for free, said Tuesday that people who haven’t either reached the upper tiers of its Rapid Rewards loyalty program, bought a business class ticket or hold the airline’s credit card will have to pay for checked bags.

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The airline did not outline the fee schedule but said the new policy would start with flights booked on May 28.

“We have tremendous opportunity to meet current and future customer needs, attract new …