She succeeds Joe Fitzpatrick, who “resigned” after the FM made a public apology for drugs deaths to parliament.
Joe FitzPatrick lost his post in the government over drug deaths hitting a new record level.
Ms Gougeon, whose appointment is viewed by many as “a poison chalice,” moves across from the rural economy brief, which will now be filled by Ben Macpherson.
First Minister Nicola Sturgeon said the Angus MSP would play a “key role” in the team fighting the pandemic.
She will report to Health Secretary Jeane Freeman, who the government said was “taking the lead” on the delivery of the vaccination programme in Scotland.
- Minister loses job over Scotland’s drugs deaths
The previous public health minister – Mr FitzPatrick – was removed from the post on Friday after Ms Sturgeon branded the government’s record on drug deaths “indefensible”.
Ms Gougeon – who was first elected as the MSP for Angus North and Mearns in 2016 – is to replace him as part of a wider reshuffle of the junior ministerial team.
The new rural affairs minister, Ben Macpherson, was previously the minister for public finance and migration.
That role has been broken up, with the migration elements to be covered by Europe minister Jenny Gilruth and the public finance brief by trade and investment minister Ivan McKee.
Meanwhile former communities and education secretary Angela Constance is to return to government in a new role of drugs policy minister, subject to a vote of MSPs on Tuesday.
Ms Sturgeon said the changes “ensure that we have a ministerial team fully focused on tackling the many important challenges facing us”.
She said: “Mairi Gougeon has proven herself to be a highly effective rural affairs minister working with stakeholders, balancing competing interests and taking on difficult policy challenges.
“She will now be part of the team protecting and improving Scotland’s public health, and will play a key role in the pandemic, taking the lead on testing.
“Mairi will work alongside the new minister for drugs policy Angela Constance, who is tasked specifically with tackling what is another major public health emergency in Scotland.”
As well as the Covid testing programme, Ms Gougeon will have responsibility for sport, child and maternal health, public health improvement and problem alcohol use and recovery.