He is a joint citizen of both the UK and New Zealand.
Brexit negotiations start on Monday, while Mr Falconer will begin in his role later this summer.
International trade secretary Liam Fox said the appointment shows the UK is "attracting the very best global talent" to "further build our trade capacity".
The new chief has also been made a head of profession - a term which indicates trade negotiation will be deemed a separate "profession" within the civil service.
That designation indicates the staff are specialists with their own clear career path and training opportunities, rather than generalists who move around different parts of Whitehall.
At a conference in London in April Falconer argued that Britain should seize the moment to inject some fresh impetus into the WTO, revitalising efforts to promote free trade around the world.
I'm absolutely delighted to join this hugely exciting new journey.
"The WTO has plateaued because it hasn't got the kind of leadership and innovative thinking that will take it to the next level," said Falconer at the prosperity UK conference. "The UK now has a unique opportunity, within the WTO, to provide economic leadership for the world trade agenda - and my God, doesn't the world need that right now.
"Many of the leading economies in the world have lost the plot. An economy like the UK is going to be an independent and powerful voice for reform and change in the global economy, and that is going to be a massively refreshing political voice in Geneva [at the WTO's headquarters]."
Britain has to set up its own schedule at the WTO - the terms on which it applies tariffs and quotas - by taking a chunk of the EU's schedule. Falconer told the conference that Britain will have to reassure the non-EU members of the WTO that none of them will be worse off under the new arrangement, most likely by setting the schedule in line with historic trading levels.