She will succeed Joanne Wilson, who will be leaving the company in the near future.
The company will confirm her joining date in due course.
In the new role, Napier will be responsible for the company's finance function across all markets in which it operates, as well as chairing the ESG Committee.
Simon Litherland, chief executive officer of Britvic, described Napier as "a strong addition to the Britvic board and executive team".
"Rebecca brings a wealth of commercial, regulatory, and international experience, which, coupled with her financial and leadership expertise will be invaluable as we continue to successfully grow our business," he added.
Napier held various finance roles at British Airways for the past 16 years. She is currently serving as its chief financial officer.
During her stint with British Airways, she also served in roles for the International Airlines Group (IAG) entity.
She sits on the boards of IAG Loyalty and IAG Cargo, in parallel to her role with British Airways.
Napier is a chartered accountant and commenced her career at Deloitte before joining the audit team of British Airways.
At the time, the airline company was listed in both the UK and the US.
Commenting on her new role, Napier said, "I am very much looking forward to joining the Britvic team as the company continues to deliver value across people, planet, and financial performance metrics for all its stakeholders."