The question will be included in the regular household surveys of the Office for National Statistics from Apr under David Cameron's scheme to create Britain's first national "happiness index", The Telegraph reported.
The ONS said other questions will seek to gauge people's overall "life satisfaction" as well as their levels of happiness with their jobs, income, housing and leisure time.
The answers will be included in the overall well-being index, alongside other measures, which are still being developed.
The Prime Minister launched the programme last November in an attempt to create a broader measure of Britain's success than the performance of the economy.
He believes governments have a legitimate role in helping people "feel better" and that the national well-being index should help politicians and wider society "build a better life".
The ONS said 450,000 would be asked four new questions over the course of the next year as part of its integrated household surveys.
The ONS will combine results from surveys with objective data, such as crime, employment and life expectancy rates, to give "a more complete picture" of the nation's well-being.