This comes after the minister rebuffed calls for him to step down earlier this week.
These had intensified in the wake of an employment tribunal which ruled in favour of former medical director Dr Rosalind Ranson.
Chief Minister Alfred Cannan said: ‘It is with regret that I have accepted Mr Ashford’s resignation as Treasury Minister.
‘I would like to place on record my thanks for the contribution he has made in establishing the new administration and indeed for the contribution he made during the Covid-19 pandemic as Health and Social Care Minister.
‘David has always played a full active role in the business of government and I commend his commitment to the roles he has undertaken.
‘I fully respect the decision he has reached and wish him well as he returns to the backbenches.’
In the tribunal report, Mr Ashford was described as ‘not always consistent’ in his evidence, and as overly reliant on former DHSC chief executive officer Kathryn Magson.