Sir Paul retired in 2022 after more than nine years as secretary general of St John International, the supporting body for all St John Ambulance establishments in over 40 countries.
Prior to this, he spent 38 years in the Royal Navy.
Dyfed Edwards, chair of Betsi Cadwaladr University Health Board, said: ‘We are delighted to welcome Paul Lambert to the Board. His extensive experience in finance, governance and leadership will bring great value to our organisation and to health and well-being services across North Wales.'