New Prime Minister Theresa May appointed the former London mayor head of British foreign policy in her first cabinet after Britain voted to quit the European Union.
One of the leading figures in the Brexit campaign, Johnson was once seen as a possible prime minister himself, but failed to win the support of party colleagues.
Washington was disappointed when Britain voted to leave the EU and Kerry has called for a careful exit process that does not damage Western unity or the world economy.
"The secretary and Foreign Secretary Johnson agreed that the US-UK special relationship is as essential as ever," State Department spokesman John Kirby said.
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"They pledged to work closely together as NATO allies to address the full range of challenges we face and to meet our responsibilities around the world," he added.
"The secretary stressed US support for a sensible and measured approach to the Brexit process and offered to stay engaged as the UK government develops its plans."
Kerry will meet Johnson this weekend, when foreign ministers gather in Brussels for a policy forum, and is due in London on Monday for crisis talks on Syria and Yemen.