Around 980 jobs will go from the BBC's professional services division -- which includes strategy and distribution, legal, finance, property, BBC people and marketing -- with a further 750 being outsourced.
The cuts in professional services will see a 46% reduction in headcount as some posts go through staff turnover, others through redundancy and outsourcing.
Thompson also confirmed reports that overall costs savings across the BBC are set to be higher than expected, coming in at £355m compared with the £320m originally mooted.
The BBC has said that the first round of cuts as part of the shake-up of the corporation will deliver £139m savings a year by 2008, which will be reinvested into programmes.
In December, Thompson confirmed that 2,900 jobs were to go at the broadcaster, and 1,800 staff are to be moved north to Manchester as part of a far-reaching restructure of the corporation. It is believed that up to 6,000 jobs could be axed in total.
Thompson said: "In December, I talked about the creative prize for the BBC and our audiences -- but the cost is nothing short of transformation.
"We have made a strong start, showing we are serious about change and ensuring we are maximising the value of our income for audiences' benefit."
He added that the BBC needed to become a simpler, more agile operation, ready to take the creative lead in a very different, very challenging digital future.
Thompson told senior staff that the BBC governors had endorsed the plans but would consider these and further savings plans from the content and output divisions as a whole at their meeting next week before giving final approvals.
The announcements come a week after publication of the government's Green Paper on the BBC's Royal Charter, which secretary of state Tessa Jowell described as a "blueprint for a strong, independent BBC" and guaranteed the licence fee for another 10 years.
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