Exact numbers are hard to come by. The United States does not keep track of emigration, and counts of Americans abroad are thus only available courtesy of statistics kept by the destination countries.
As of June 2016, the State department's consular section estimated that there are 9 million non-military U.S. citizens living abroad,[3][4] an increase from the 4 million estimated in 1999.
The above includes many retirees, who find their retirement incomes stretch further abroad. But, it also includes a lot of PHD students who have troubles finding academic jobs inside the US etc.