Fathers are nearly two years older at the birth of their children than two decades ago, while women are having fewer babies than the generation before them.
Britain's Office for National Statistics (ONS) said the average age of fathers in England and Wales on the birth of their son or daughter is 32.9, up from 31.1 in 1993.
It echoes the trend of delaying parenthood in mothers, with figures in October showing 30 was the average age for women giving birth - a record high.
The figures also show men aged 30 to 34 had the highest fertility rate last year, matching their female counterparts.
Previously, men in their mid-to-late 20s had the highest fertility rate but were overtaken in 1993 by men in their early 30s.
The ONS said 62pc of babies born to married parents or partners had fathers aged 30 to 39.
The average completed family size for women born in 1968 and reaching 45 in 2013 was 1.92 children. This compares with their mothers' generation, represented by women born in 1941, who had on average 2.34 children. Two children was the most common family size for women born in 1941 and 1968.
Only one in 10 women born in 1968 had four or more children, compared with nearly one in five women born in 1941.
Women born in 1983 have had slightly fewer children on average (1.02) by their 30th birthday than women born in 1968, who had 1.15.