Clarke’s initial contract was due to expire at the end of the current World Cup cycle.
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.”
Clarke has had to reshuffle his backroom staff after assistant Steven Reid and goalkeeping coach Stevie Woods stepped down because of club and family commitments.
Former England and Rangers player Chris Woods replaces Woods while Aston Villa set-piece coach Austin MacPhee also joins John Carver in the backroom team.
Clarke said: “Austin has major tournament experience with Northern Ireland and now a respected set-piece coach in England’s Premier League.
“He is a specialist coach and his approach to coaching on the field and use of data off it will be an asset to the existing backroom staff.”
Clarke has brought Zander Clark, Liam Kelly and Lewis Ferguson into his squad for the World Cup qualifiers against Denmark, Moldova and Austria.
St Johnstone goalkeeper Clark has won his first call-up while Motherwell’s Kelly returns to the squad with David Marshall and Jon McLaughlin dropping out.
Aberdeen midfielder Ferguson comes in as Scott McTominay misses out after Manchester United manager Ole Gunnar Solskjaer revealed earlier this week he was struggling with injury.
Kenny McLean returns after missing Euro 2020 with a knee injury while John Fleck also drops out.