Shares in Lloyds, owner of Bank of Scotland, closed the day down 2.71p, or 3.5%, at 74.65p after the Treasury offloaded a 6% stake at 75p a share, netting it £3.2bn.
The share price fall cut Lloyds's market value by £1.9bn to £53.3bn.
Demand among institutional investors for the Government's shares, at a price 3% below Monday night's closing mark, was almost three times the number on offer.
The Government will consider offering shares to private retail investors in future, Mr Osborne said.
"This is the first in a multi-staged sale programme. I will consider all options for later sales of our shareholding in Lloyds, including a retail offering to the general public," Mr Osborne said in a letter to Andrew Tyrie, chairman of the Treasury Select Committee.
The stake sale comes five years after Lloyds was bailed out in the wake of its rescue acquisition of Edinburgh-based Halifax Bank of Scotland.
Some in the City now think that the Government could sell its remaining 32.7% stake before the General Election due in 2015.
Ian Gordon, analyst at Investec, said: "We regard the Government's timing as impeccable, and it appears credible to suggest that it could yet be out in full by the election."
But there is still some scepticism in the Square Mile about the rise in the Lloyds share price, which has doubled in the last year, when the bank has only recently returned to profitability under chief executive Antonio Horta-Osorio.
Shailesh Raikundlia, analyst at Espirito Santo said: "We believe that the shares have been buoyed by this upcoming placing as a sign of confidence the group is returning to profitability and the recent policy actions by the Government of the Help-to-Buy scheme to revive the mortgage market."
During 2008's bailout, the Government purchased Lloyds shares at an average price of 73.6p, meaning it will make a profit of £61m from this first sale, although this does not take into account the cost of leaving the money tied up in Lloyds shares since 2008.
The sale came just days after Lloyds agreed to boost the profits of TSB, the brand name for the 631-strong branch portfolio it plans to float on the stock market next year, by some £200 million over the next four years. The move is intended to help smooth the negotiating process with the European Commission which wanted it to sell the business by November this year.
It is thought that American investors snapped up 30% of the Lloyds share offering. If this US interest in UK banking paper endures, it will be good news for Barclays which is seeking to raise nearly £6bn from investors to bolster its capital cushion.
A sale of the taxpayer's stake in RBS is unlikely soon.
Its shares closed at 362.5p last night, down 4p or 1.1% on the day. This is 27.8% below the 502.26p price the Government bought in at.
The position of RBS, which is 81% owned by the taxpayer is complicated because the Government has hired investment bank Rothschild to investigate whether the Edinburgh bank should be broken up. A decision is expected in the autumn.