The decline of fertility is one of the most fundamental social changes that happened in human history. It is therefore especially surprising how very rapidly this transition can indeed happen.
This chart is an excerpt of the data-entry on fertility which shows much more data and explains why fertility is declining.
As we see from the chart below it took Iran only 10 years for fertility to fall from more than 6 children per woman to fewer than 3 children per woman. (Iran made this transition under a conservative Muslim government.)
We also see from the chart that the speed with which countries can achieve low fertility has increased over time. A century ago it took the United Kingdom 95 years and the US 82 years to reduce fertility from more than 6 to less than 3. This is a pattern that we see often in development: those countries that first experience social change take much longer for transitions than those who catch up later: Countries that were catching up increased life expectancy much faster, they reduced child mortality more quickly and were able to grow their incomes much more rapidly.