Jobs will go in news, sport, TV, radio, learning, entertainment, drama and children's programming. Positions are either to be cut completely, outsourced or reduced through redundancy offers.
The announcement follows more than 1,700 job cuts in communications, recruitment and strategy earlier this month.
The UK's National Union of Journalists accused Mr Thompson of 'ripping the heart out of the BBC'.
"How can the BBC maintain the quality and standards it is justifiably praised for whilst axing one in five staff?" said NUJ general secretary Jeremy Dear.
"BBC staff deserve better than to be used as political pawns in what many see as an unsavoury and grubby deal between government and senior BBC management."
Of the 1,620 jobs being cut, BBC News will lose 420 posts - equivalent to 12 per cent of the department. Those cuts will save the department £34.4 million by 2008.
New Media will lose 58 staff, saving £7.7 million. As part of Mr Thompson's overall savings plan, the cuts will release £355 million for the corporation every year which will be reinvested in programming.
"We are going through the toughest period any of us can remember. It's a difficult and painful process but necessary," said Mr Thompson.
"We need to free up money to start investing in our digital future, to end our current Charter in December 2006 on budget and to show we are serious about providing value for money."
The BBC's technology group and global news services, including its network of international news websites, will not be affected.
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