A statement from the Scottish FA was released moments after Croatia's win over Ghana on Saturday confirmed Scotland's elimination. Clarke and the squad were still at their Charlotte base when the players were informed of his decision.
Scotland's tournament ended with a single win — a 1-0 victory over Haiti in their opener in Boston — followed by a 1-0 defeat to Morocco and a 3-0 loss to Brazil in Miami. They went into the Brazil fixture with a chance of advancing as one of the best third-placed teams, but defensive mistakes ended that prospect.
Clarke wrote directly to supporters in his farewell letter.
"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," he 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."
Scottish FA chief executive Ian Maxwell acknowledged the disappointment of the exit while placing Clarke's tenure in a broader context.
"While we are all disappointed to have exited the World Cup at the group stage, we must not lose sight of the undeniable progress made during Steve's seven years in charge," Maxwell said.
"From starting as a pot four team in 2019 to topping our World Cup qualifying group, he has more than delivered on the remit to take Scotland back to a major tournament. We thank Steve for his record-breaking contribution and know that when the disappointment of World Cup elimination subsides, the Scotland supporters will be thankful for the memories of marching with pride at major tournaments once again."
Clarke leaves with Scotland having qualified for two European Championships and this World Cup — a remarkable run of qualification from a nation that had previously failed to reach a major tournament for more than two decades.