Few weeks ago, The Economist magazine published a short piece on the world's shifting centre of gravity*. The map is based on this study by the McKinsey Global Institute.
According to the study, "the centre is rapidly shifting east—at a speed of 140 kilometres a year and thus faster than ever before in human history". As you have already guessed, the main reason for this is rapid urbanisation in developing countries, in particular China.
*The global center of gravity is calculated weighting the approximate centre of landmass of the world by countries' GDPs.
The Census Bureau of the US also calculates the National Mean Center of Population. This is the animated map displaying the evolution of its position (and here is a different static version of the map).
PS. Dear readers, my life is undergoing some major (good) changes so I'm out of time to post. I hope you don't mind a 'replay post'!