It is the first acquisition by the fifth-generation bakery business, which was established in a grocery shop in 1876.
A spokesperson for the firm said the acquisition represented “a great opportunity for business diversification and development”.
Giles Foods – also a family-run business – produces unbranded baked goods, including garlic breads, dough balls, French and Italian breads, Danish pastries, tarts and buns, which are sold to retailers, restaurants, pub chains and catering companies.
It produces 137 product lines, has 300 employees across two sites in Milton Keynes and Warminster, and an annual turnover of £26m.
Warburtons will run Giles Foods as a separate business, with the current management team remaining in place.
Jonathan Warburton, chairman and chief executive of Warburtons, said: “This agreement with Giles Foods underlines our continued commitment to growth, diversification and ultimately, creating quality products which we know people love.
“As well as being a family-run business, Giles Foods has a strong track record in innovation and anticipating the tastes and demands of consumers. Alongside Warburtons, this will help us continue to work towards consolidating our position as one of the world’s best family food businesses.”
David Rixon, managing director of Giles Foods, said: “There was an enormous amount of interest from a broad range of potential partners, but Warburtons, with its heritage and values, ultimately made the decision very straightforward. We are confident that becoming part of the Warburtons business will allow what Giles Foods has done for 35 years to evolve and grow.”