Ms Evans was criticised by the Holyrood committee that investigated her handling of the complaints against Mr Salmond.
Her contract was extended during the period between the judicial review and Mr Salmond’s criminal trial, where he was cleared of 13 allegations of sexual assault, but is due to expire in March.
It is believed her replacement will be in place before the end of the year to allow for a handover period.
A Scottish Government spokesman said: “The permanent secretary’s planned departure is already in the public domain. As previously confirmed, Leslie Evans’ tenure concludes in March 2022 and she will leave the civil service at that point.
“In line with normal timescales, recruitment to appoint the new permanent secretary to the Scottish Government will commence shortly, with interviews expected to take place in early autumn and a successful candidate announced in due course.”
He added: “The permanent secretary, along with her executive team, is firmly focused on supporting the government’s ambitious plans for its first 100 days and manifesto commitments, continuing to the lead the civil service as it responds to Covid-19 and manages recovery.”
A number of senior government figures came under fire from Mr Salmond, who in March, said he would take legal action against Ms Evans. Of them, only one, former Lord Advocate James Wolffe, has since quit, to be replaced by Dorothy Bain QC.
Nicola Sturgeon’s chief of staff Liz Lloyd is on leave – temporarily replaced by head of policy Colin McAllister as acting chief of staff.
Jackie Baillie, Scottish Labour’s deputy leader and a member of the Holyrood committee, said: “The departure of such a senior figure shows that the Scottish Government admit their handling of the Salmond fiasco was not fit for purpose. The First Minister has shown a serious failure of judgement in not asking Evans to consider her position.”
Scottish Conservative MSP and inquiry member Murdo Fraser said: “Whoever replaces her as the permanent secretary must be prepared to stand up to SNP ministers and commit to being fully transparent with the public over government decision-making after so many failures in recent years.”
The Civil Service Commission regulates recruitment to the Civil Service, providing assurance that appointments are on merit after fair and open competition.
A Civil Service Commissioner chairs selection panels for all external recruitment competitions at permanent secretary level. The First Minister makes the final decision, following consultation with the head of the civil service and the First Civil Service Commissioner.
The post will be advertised widely – internally, externally and to other government departments – while is understood that Ms Evans’ replacement will be in place by the end of the year.