The 55-year-old replaces Alex McLeish on a three-year deal just a day after securing third place in the Scottish Premiership for his Kilmarnock team.
The former West Brom manager, who won the PFA Scotland and Scottish Football Writers’ Association manager of the year awards, has signed a three-year contract until the end of the 2022 World Cup qualifying campaign.
“I firmly believe we have a talented group of players who can achieve success on the international stage,” said Clarke, who won six caps for Scotland as a player.
“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.”
Scottish FA chief executive Ian Maxwell said: “Steve’s pedigree as a coach and manager of the highest regard set him apart in a high-calibre group of candidates.
“This season’s achievements simply reaffirm the credentials we believe will be of huge benefit to the Scotland national team.
“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.”
McLeish was sacked last month after a dismal start to the Euro 2020 qualifiers, which included a 3-0 defeat by Kazakhstan.
Scotland are fifth in their group after two games while Kerr’s side are set for next month’s Women’s World Cup in France.
Scotland’s men’s team have not qualified for a major tournament since the 1998 World Cup.
Former St Mirren and Chelsea defender Clarke also had coaching stints with Chelsea, Newcastle and Liverpool.