The Globe theatre is sending a production of Hamlet on the first genuine world tour in theatre history. Starting on 23 April 2014, the 450th anniversary of Shakespeare's birth, the company will spend two years travelling by planes, trains, boats and buses to visit every nation on Earth – 205 countries in all.

"I think having a lunatic idea is a very good thing, it's a great way to keep everybody focused and dazzled and delighted by the ambition and energy of the company," said the artistic director, Dominic Dromgoole. "If we're going to do every country in the world it has to be every country, we're not going to leave anyone out. All the 'Stans, South and North Korea – we're very keen to get into North Korea. Antarctica? Fuck yes."

He said it had to be Hamlet for the project. "It is an iconic play, instantly recognisable anywhere. It has that capacity to question, to challenge, to inspire in any country in the world," he said.

The revered theatre director Peter Brook said it was "a bold and dynamic project", and agreed with the choice of play. "The six simplest words in the English language are 'to be or not to be'. There is hardly a corner of the planet where these words have not been translated. Even in English, those who can't speak the language will at once recognise the sound and exclaim 'Shakespeare!'"

The show will open at the Globe next April, and close there exactly two years later on 23 April 2016, which also happens to be Dromgoole's last day as artistic director.

The 204th and 205th stops are already decided: the Rift Valley in Kenya – "where human life began on Earth", Dromgoole said – and Elsinore in Denmark, the castle where Shakespeare set his tragedy. They will be performing in theatres, in town squares, on beaches and in jungle clearings. There are, however, many gaps and question marks in the plan.

The company will snake across Europe, at one point playing four countries in five days, into the Caribbean, America north and south, down the west coast of Africa, on into Australia and the Pacific islands ("logistically that could be quite hard work," Dromgoole said, looking slightly anxious for the first time) on to Indonesia, Japan, China and Asia, back up the east coast of Africa, to Elsinore and then home. Easy.

The experiment is unprecedented but builds on links forged through the Globe's last spectacular attempt to link nations through the words of the glover's son from Stratford-upon-Avon. Last summer as part of world Shakespeare season celebrating the Olympics, the Globe invited companies to come and perform every play the Bard wrote in 37 different languages – including Troilus and Cressida in Maori, Two Gentlemen of Verona in Shona (spoken in Zimbabwe and Zambia), and the Henry VI plays divided among the Balkans in Serbian, Albanian and Macedonian.

The season proved a wild success, seen by more than 100,000 people in six weeks, 80% of them first-time visitors to the Globe. "It was such a fantastic experience I thought we need to keep that energy going, we need another bananas idea," Dromgoole explained.

The touring Hamlet will be the Globe's scaled-down version, which has already been admired in UK tours, with a cast of eight – from a company of 12 to allow for illness and even the odd day off – playing more than two dozen roles between them, scampering through the text of Shakespeare's longest play in just over two and a half hours.

Although they hope to attract sponsorship, the unsubsidised main house on the South Bank has been making a handsome profit in recent years, and small-scale tours having been covering their costs or better.

Since Dromgoole launched Romeo and Juliet in a camper van six years ago – the modern version of the strolling players of Shakespeare's day arriving in a wagon piled high with props and costumes, he said – he has been trying to reach the parts other tours don't touch.

This summer he is sending a company out to play Shakespeare's history plays on the actual battlefields that sparked regime change, beginning last Sunday with Henry VI on the wide green fields in Yorkshire where in 1461 streams ran red with blood and ditches were choked with bodies at the battle of Towton.

"Touring is in our blood," Dromgoole said. "It's what Shakespeare's company did, it's what we do – and it's great fun."