The family-run firm, which is already in 24 Asda stores, will supply single sausage rolls, as well as single packs and three-packs of savoury mince pies to north-east stores.
Tesco will take between 3,500 and 4,000 products a week, which will be worth about £300,000 a year to the Sunderland-based bakery.
Partner Hilary Monk said its persistence with Tesco had paid off. "Local people know us well, but when you're a small company, it can be more difficult if a big chain hasn't heard of you," she said. "We kept calling, emailing and sending samples and of course, our sales increasing in Asda also gave us leverage."
She added: "We hope to gain contracts with other supermarket chains in the future."
Gelders also hopes the new contract will mean its 42-strong workforce can be expanded.
Sam Nundy, Tesco regional buying manager north east, said: "We're very pleased to be able to offer Gelders Bakery products to our customers. This will be a fantastic addition to our growing offer of local products across our stores in the north-east."