Beswetherick, who joined Bounty 11 years ago, will replace Simon Williamson who is stepping down after five years as managing director.
In his role as business development director at Bounty and as a member of the 2004 management buy-out team Beswetherick helped to steer the business towards the recent acquisition by US online media company Kaboose.
Kaboose acquired Bounty from private equity firm ECI Partners for £70m in November last year.
Beswetherick said: "Bounty is a business that has achieved great things over recent years, but there still remains a mass of untapped potential."
Williamson said: "I'm very proud of what we have achieved and confident that Ian's proven leadership skills combined with our excellent new Kaboose home will take Bounty to the next level."
Bounty provides information, support and products for young families through the stages of pregnancy, birth, toddlers and pre-school.
Its partners include UK maternity hospitals and FMCG brands such as Procter & Gamble, Kimberley Clark, Unilever, Johnson & Johnson and Asda.
The company is based in Welwyn Garden City, Hertfordshire, and has 633 employees.