Abell, who joined EEAST as chief executive in 2021 from Mid and South Essex NHS Foundation Trust, where he was deputy chief executive, will take up his new post in mid-July.
Abell said: 'It's been tremendous privilege to be the chief executive of EEAST and work with amazing people every day. We've come a long way in the last few years and I feel we have risen to the challenge together.
'EEAST is a much better place to work today than when I joined, and we as a team have really improved our focus on the care we provide to our patients.
'I am proud of the team we have built at EEAST and know I will be proud of how this team goes on to great achievements in the future.
'I'm not going far and look forward to continuing to work with EEAST as we continue improving our service to all the people of the east of England.'
EEAST deputy chief executive Kate Vaughton will step up to be interim chief executive while the recruitment process for a permanent replacement takes place.
Abell's previous roles include deputy chief executive and chief transformation officer at Mid Essex Hospitals, Southend University Hospital and Basildon and Thurrock University Hospitals. He has also worked in commissioning at Basildon and Brentwood CCG and was director of service improvement at Cambridgeshire and Peterborough NHS Foundation Trust.