The owner of the Evening Standard, Independent Print (IPL), will pay £1 for the titles, while INM will contribute £9.25m over the next 10 months in exchange for IPL taking on all future trading liabilities.
The news comes just a day after INM released its preliminary full-year results, which showed revenues at its UK arm were down a third, producing an operating loss of €6.9m (£6.2m).
INM said in a statement, that for 2009, the titles represented an operating loss of £12.4m and the sale would be immediately accretive to its earnings.
A cornerstone of the deal was an existing print contract with Trinity Mirror Printing and the Daily Mail & General Trust.
INM maintained that while these agreements will continue, they have been renegotiated at a lower level or for a shorter period without invoking any of fiscal penalties for early termination.
The Independent titles will continue to be printed by Trinity Mirror but under a shorter five-year contract. However, should Lebedev decide not to continue printing with Trinity Mirror after that period, the balance of the contract would remain with INM.
Neither INM nor Trinity Mirror would disclose terms of the contract such as value or duration, but a spokesman for the former said that Trinity Mirror was "clearly keen to protect its rights".
Trinity Mirror director of manufacturing, Rupert Middleton, said: "We are delighted that the future of the Independent has been secured. After a long and successful relationship with the group we look forward to serving the new Independent going forward."
INM will also have real-time access to editorial content at the newspapers under a commercial agreement, which would continue to be produced at the current DMGT-owned Kensington offices.
Chief executive of INM Gavin O'Reilly said that the company would now focus on its assets outside of the UK and that he had faith that "the Lebedevs will be progressive and supportive ownder of the Independent titles. which have played such an important role in British public life for nearly 25 years".
INM shares were up a fifth to 12 eurocents in intraday trading at the time of writing.
Lebedev buys INM's Independent titles for 1
Independent News and Media (INM) has announced the sale of its loss-making title The Independent and The Independent on Sunday to Alexander Lebedev.