Lady Poole gave notice on Friday of her intention to step down from the key post for personal reasons.
It comes 10 months after her appointment was announced, with Deputy First Minister John Swinney saying in December last year that Lady Poole was “highly qualified for the demanding task put in front of her”.
Mr Swinney said he was “grateful” for the “important work” Lady Poole had done since then with the Scottish Covid-19 Public Inquiry.
She has also offered to assist her successor while serving her notice period, the Deputy First Minister added.
Mr Swinney stressed the work of the inquiry was continuing, adding that he had already spoken to Scotland’s most senior judge, Lord Carloway, the Lord President of the Court of Session, about a new appointment.
The Deputy First Minister said: “I am grateful to Lady Poole for the important work she has undertaken since the establishment of this inquiry, and for her offer to assist with the transition to her successor during a notice period of up to three months.
“I thank Lady Poole for her work and wish her well.
“I have already spoken with the Lord President about arrangements for appointing a new judicial chair for the independent inquiry.
“The inquiry team has been drawing in key information as part of the important evidence-gathering process which precedes inquiry hearings, and that work is continuing.
“The Scottish Government, and I know the independent inquiry team, remain committed to this vital exercise, and people who wish to can continue to engage with the inquiry.
“I will provide a further update to Parliament about a replacement chair at the earliest possible opportunity.”
The inquiry was established by the Scottish Government and will run alongside a UK-wide inquiry.
It has already been confirmed that the Scottish inquiry will look at areas such as pre-pandemic planning, the decision to enter lockdown, the supply and distribution of personal protective equipment (PPE), and how coronavirus was dealt with in care homes.
It will mainly deal with the three years from January 1 2020 to December 31 2022, although it will look at pandemic planning work carried out before then.
A spokesperson for the Scottish COVID-19 Inquiry said: “As far as possible it will be business as usual and the Inquiry will continue its important work pending the appointment of a new Chair.”