See: The Battle of Bretton Woods. It really is pretty fascinating.
A more useful answer is inertia.
After England's Sterling lost its place as reserve currency for the world, the USA's massive gold reserves (>50% of the world's holdings) let the US peg the Dollar to gold and everyone else pegged their currency to the Dollar (aka the Bretton Woods system).
Of course, (puts on flame suit) because gold standards are actually a terrible idea, the USA's overprinting of cash ended up causing exchange rate imbalances and Europeans started cashing in their dollars for gold.
So Nixon ended the gold standard and inertia + economic strength and maneuvering has kept the Dollar as the global reserve currency for 43 years.