White, 58, leaves at a time the Scottish firm has benefited from higher pricing, as well as seeing strong trading performance across its soft drinks divisions.
The Cumbernauld-headquartered group said White will resign as a director and retire from the company, which he joined in 2002 as managing director.
Separately, the drinks company said it expects annual profit performance to be marginally above the top end of analysts' expectations.
A.G. Barr said revenue for the first-half period ended July 30 was expected to be about £210 million (€245 million), a 10% increase on a like-for-like basis.
The company said that the group's medium-term plan to rebuild its operating profit margin was 'progressing well'.
'A Year Of Investment'
"In March we communicated that 2023/24 would be a year of investment across the business, supporting the group's long-term revenue and profit growth ambitions," White said. "I am pleased to report we have had a strong first half, despite ongoing macro cost challenges. Our focus remains on offering consumers great value, affordable brands.
"Our medium-term plan to rebuild the group's operating profit margin is progressing well across a range of activities, including supply chain optimisation, cost management and portfolio development.
"We have strong brand plans in place across the business for the balance of the year to sustain our growth momentum and we remain confident in the group's long-term growth strategy".