When the Great Depression hit in the United States, the prevailing laissez-faire (I don't know if you learned about the "robber barons" in school, but think those guys) economic consensus largely collapsed, and with FDR the US embraced Keynesianism - think New Deal central planning. Europe embraced social democracy. In reaction to this, a bunch of guys such as Friedrich Hayek, Ludwig von Mises and Milton Friedman set up the Mont Pelerin Society to resist ideas of state intervention in the economy. You can trace neoliberal economic consensus largely back to these guys.

So it is very similar to libertarianism, as it should be, since neoliberalism and libertarianism both look to classical liberal economics for influence, and most of those Mont Pelerin guys are loved by libertarians.

But as Norm_Chumpsky said below, neoliberals are very pro-imperialist, and they still see a use in the state for expanding free markets abroad. Libertarians are not as pro-intervention. But they both draw from largely the same ideology and same thinkers.

This is my amateur take.