Clarke was appointed in the summer of 2019 and led Scotland to their first major tournament since the 1998 FIFA World Cup in France by qualifying for EURO 2020.
Scotland exited EURO 2020 at the group stage after picking one point from their three group games and will now turn their attention to qualifying for the Qatar 2022 FIFA World Cup.
Scotland are second in their World Cup qualifying group after three games and take on leaders Denmark, Moldova and Austria next month.
Clarke told the Scottish Football Association website: "Firstly, I am proud to extend my stay as Scotland head coach and I look forward to working with my staff and players as we look to continue improving as a team.
"Being involved in Euro 2020 has given us all an added determination to return to a major tournament again as quickly as possible.
"I said in the dressing room after the Croatia game that we all had to learn lessons from playing at the Euros and to come back stronger.
"I am committed to helping us return to a major tournament as quickly as possible and improving on what we have achieved until now.
"The players and my staff share that determination and the hard work resumes next month."
