The precise limit will be set in the spring of 2014, and the cap will be imposed a year later.
He said the limit on total welfare spending would be set by the chancellor at the beginning of each parliament, and MPs would be asked to support it.
If the limit was breached, the chancellor would have to explain why, and a vote would be held in Parliament.
Mr Osborne explained that benefits which fluctuate with the economy, such as Jobseeker’s Allowance, would be excluded from the cap.
So too will spending on the basic state pension.
“All other benefits, from tax credits to income support, to the vast majority of housing benefit, will be included in the cap,” he told MPs.
In 2014, the government is expected to spend £112bn on welfare payments, rising to £113.1bn in 2015, and £117.9bn in 2016.
“The principle is clear,” said Mr Osborne. “The government has a responsibility to taxpayers to control their spending on welfare; and Parliament has a responsibility to the country to hold the government to account for it.”
Labour has already said it will introduce a three-year cap on welfare spending, if elected in 2015. That cap would also include housing benefit.