The chancellor said the Royal Mail shares money – valued at £1.5bn – would be used to pay down the national debt reports BBC.
The £3bn in cuts come ahead of further reductions to be announced in July.
The NHS, schools and overseas aid are protected from cuts – but other departments such as the Home Office and MoD will have to find savings.
Labour accused Mr Osborne of “ripping up” his long term economic plan by springing the announcement on MPs.
The SNP said the move “poses real danger to the postal service and, in particular, the universal service obligation which is of huge importance to Scotland”.
The government is committed to clearing the deficit by 2018/19 without increasing income tax or VAT, something Mr Osborne said would not be “easy”.
He needs to find a further £30bn of savings over the next three years, including £12bn to come out of welfare spending and £13bn from cuts to government departments.
Former Labour leader Ed Miliband made his first Commons speech since losing the general election in the debate on the Queen’s Speech, urging the chancellor to ensure David Cameron followed through “on his one nation rhetoric”.