The star Brexit campaigner said he was "humbled" having been named the new foreign minister and is expected to work closely with India in his role that covers the Commonwealth countries, alongside newly-appointed global trade minister Liam Fox.
Britain's new foreign secretary, Boris Johnson, has a long history of making provocative and sometimes insulting comments that are distinctly undiplomatic in their tone.
In a sign of the difficulty Mr Johnson may face in building bridges with opposite numbers around the world, French foreign minister Jean-Marc Ayrault told Europe 1 radio: "I am not at all anxious about Boris Johnson, but you know his style, his method during the campaign".
European leaders have pressed her to move quickly in implementing Brexit, amid fears of the damage the continued uncertainty could do to the EU and the world economy.
Russian President Vladimir Putin said he was ready for "constructive dialogue" with Britain's new premier, while White House spokesman Josh Earnest said United States officials who had worked with May "found her to be quite effective".
In April Boris Johnson said that U.S. President Barack Obama opposed Brexit because of his part-Kenyan heritage gave him, in Johnson's words, an ancestral dislike of the British Empire.
He said he had received a call from US Secretary of State John Kerry, who called for "more Britain abroad".
"After a vote like the referendum result on June 23, it's inevitable that there is going to be a certain amount of plaster coming off the ceilings in the chancelleries of Europe", Johnson said.
The appointment of a man who in the run-up to the referendum compared the goals of the EU with those of Adolf Hitler and Napoleon is likely to cause consternation in European capitals.
The foreign ministers of Latvia, Estonia and Norway were others who said they looked forward to meeting Johnson.
The U.S.-born, part-Turkish Johnson said Britain was quitting the European Union but "that does not mean in any sense leaving Europe".
Work and pensions minister Stephen Crabb, who had also sought the prime minister's job, resigned citing family reasons, days after the married politician had hit the front pages for allegedly sending flirtatious WhatsApp messages to a young woman.
Reports added that outgoing Prime Minister David Cameron was given a resounding ovation by Conservative MPs as he exited 10 Downing Street. German Finance Minister Wolfgang Schaeuble said Thursday: "We must let Her Majesty's new government have a bit of time to make the necessary decisions".
Veteran lawmaker David Davis was appointed to the newly created post of secretary of state for exiting the European Union, leading overall Brexit negotiations.
Juergen Hardt said that "free access to the common market means, among other things, accepting other fundamental freedoms such as the freedom of movement".
Still, Hardt suggests: "Britain remaining in the European Union should also be an option for the new government - it would be better for Great Britain and the rest of the European Union".
"The number one challenge is to stabilize the economy, send signals of confidence about the future, the plans we have for the future, to the markets, to businesses, to global investors", Hammond told Sky News.