The 55-year-old succeeds Alex McLeish at the helm, who was sacked by the SFA back in April following a string of poor results .
Clarke guided Kilmarnock to third in the Scottish Premier League this season and oversaw a 2-1 win over Rangers on Sunday before hinting at a summer departure.
He stated post-match: "In my time at Kilmarnock, I'm sorry I didn't win you a trophy but I stand here in front of three stands of Kilmarnock supporters - that is my trophy."
Scotland have appointed Clarke on a three-year contract, with the team currently sitting fifth in their Euro 2020 qualifying group after two games.
His first match in charge is scheduled against Cyprus on June 6, before a trip to Belgium three days later.
"It is an honour," he said. "I firmly believe we have a talented group of players who can achieve success on the international stage. I look forward to working with them and helping them to fulfil those ambitions.
"I appreciate the Scotland supporters have waited a long time for the national team to qualify for a major tournament. Now we have a Women's World Cup to look forward to in France this summer and it's my motivation to emulate the success of Shelley Kerr and her squad by leading us to Euro 2020.
"I believe we can qualify and look forward to that journey with the players and the fans, starting against Cyprus and Belgium next month."
Clarke was named PFA Scotland Manager of the Year for his exploits at Kilmarnock this season and had one year remaining on his contract with the club.
After arriving at Rugby Park in October 2017, Clarke managed to take the team from second bottom in the Premiership to fifth and built on that success in his second year at the helm.
Scottish FA chief executive Ian Maxwell also offered words of praise for the new national coach, as he stated: "I am delighted that we now have the country's deserved Manager of the Year to lead the Scotland national team and his experience over the past two decades will be integral to rejuvenating our UEFA Euro 2020 qualifying campaign, which resumes next month.
"It was important that we undertook the recruitment process diligently and respectfully, especially given the importance of the final games of the domestic season for Kilmarnock, Steve and his players."