She will take up the reins on 1 September, replacing outgoing acting chief executive David Snowball.
Snowball was appointed to the position on a temporary basis in June last year after the previous chief executive, Richard Judge, went on "special leave" before officially stepping down two months later after four years in post.
Snowball will retire from the HSE at the of the year.
Albon has worked at the London-headquartered Insolvency Service since February 2015, implementing its strategy to improve service to its customers, lower its costs and strengthen the UK's insolvency regime.
The government department is an executive agency of the Department for Business, Energy and Industrial Strategy, responsible for administering compulsory company liquidations and personal bankruptcies, and dealing with misconduct through investigation of companies and enforcement.
Albon's previous roles in government include: director of strategy and change at HM Courts and Tribunal Service; director of civil family and legal aid policy at the Ministry of Justice (MoJ); deputy director of criminal legal aid strategy, MoJ; and she has also service as principal private secretary to two Lord Chancellors.
Albon said: "I am honoured to have the opportunity to lead the executive of this important and hugely respected regulator. Working together with my new colleagues across HSE, I'm looking forward to getting to grips with the vital mission we deliver on behalf of Great Britain's workplaces. My focus will be on continuing to deliver improvements in health and safety performance as our workplaces move into a future with new challenges, new technologies and new opportunities."
Martin Temple, HSE chair, added: "I am delighted to welcome Sarah Albon to HSE as our new chief executive and look forward enormously to working with her.
"Sarah's CV speaks for itself and her valuable experience in leading organisations through change and planning for the future will stand her in good stead leading this world-class regulator of workplace health and safety."
The appointment was made following an open recruitment process.