New Prime Minister Liz Truss has stuck with Mr Jack, 59, who was first appointed by Boris Johnson in July 2019.
Tweeting the news on Tuesday night, Mr Jack said: “I am honoured to be reappointed Secretary of State for Scotland.
“Liz Truss has been clear she will deliver for people right across the UK. I look forward to being part of her new Cabinet as we tackle the challenges facing our country.
“I am very pleased that I will be continuing in my role in delivering an ambitious UK Government programme in Scotland.”