The 62-year-old ends a seven-year reign in which he led Scotland to their first men's World Cup in 28 years, in addition to back-to-back European Championship qualifications.
Scotland finished third in Group C but were not among the top eight third-placed teams to progress to the knockout rounds. They faced Haiti, Morocco and Brazil in the group.
"The country's most successful national coach has called time on his seven years in charge following confirmation of Scotland's exit from the 2026 FIFA World Cup," the Scottish FA said in a statement.
In May, Clarke signed a new contract to remain in charge until the 2030 World Cup and was also set to lead Scotland at Euro 2028, which will be co-hosted by Britain and Ireland.
"The most emotional part of this goodbye is for my players, without whom we wouldn't have had any of the memories that we've accumulated from 2019 until now," Clarke said.
"They deserve all the praise and adulation that they receive and it was truly an honour to be called their Gaffer.
"Thanks for having me and good luck to my successor."