Designed by Turner Prize-winning artist Anish Kapoor, the swirling, rollercoaster track-like steel structure will stand 115 metres tall - 22 metres taller than the iconic New York statue.
Called The Orbit, the sculpture is set to be the United Kingdom's biggest piece of public art at a cost of $31 million.
Mr Johnson rejected claims that Britain was "nuts" to be unveiling such an ambitious piece of public art after only just scraping out of recession.
He said the tower could be described as: "A giant treble clef, a helter-skelter, a super-sized mutant trombone. Some may even see the world's biggest-ever represenation of a shisha pipe and call it the hubble-bubble."
Love it or hate it, it will be a conversation piece, and Mr Johnson says London's Olympic city needed something to be remembered by.
"We thought if Brussels could have the Atomium, remember, for the World Fair in Brussels ... the world's most inaccurate model of a carbon molecule but still visited by thousands of people, hundreds of thousands of people, only Paris could have the Eiffel Tower, then we thought our great Olympic site had to have something," he said.
Mr Johnson is well aware Britain has just had a close shave with recession but he defends the artistic expense and hopes the $31 million Orbit will represent the dynamism of a country emerging from recession.
"I know very well there will be people who will say we are nuts, we are barmy, in the depths of a recession, to be building Britain's biggest piece of public art," he said.
"Now's a fantastic time. Now is a fantastic time. The Olympic effort is helping to keep the British construction industry going."
Informed by AM that Australia has a soft spot for London's ever-unpredictable, larger-than-life mayor, he replied: "Australia loves me? G'day Australia!"
"Can I just say hello to all my cousins, Mark and Paul and James and Stephen and Jenny Lynne and everybody else."
"I don't think this is a crazy stunt. I want to be absolutely clear," he added.
"This is a very hard-headed venture. We need to justify huge amounts of money that we are investing in east London and so we need to make sure people come to east London for generations to come and look at this thing, and go up it, and then go and shop at Westfields and hang out."
For his part, Kapoor says the tower is the "commission of a lifetime".
"I am deeply honoured to be invited to undertake this challenging commission," Kapoor said.
"I am particularly attracted to it because of the opportunity to involve members of the public in a particularly close and personal way."
About 700 people an hour should be able to go up the tower, which will give views over the stadium in Stratford, east London, and the surrounding Olympic Park.
Kapoor was born in Mumbai and educated at art college in Britain before forging a career as one of the world's most distinctive sculptors, winning the Turner Prize in 1991.