The decision follows the Secretary of State for Transport's provisional approval last year. Mr Bowis said:
'We have now had a chance to look further at the environmental impact of the scheme at a number of locations along the proposed extension.
'We are satisfied that the scheme as now approved includes sufficient measures to protect neighbouring properties.
'However, it is now for London Underground to consider how the scheme might proceed under the Private Finance Initiative, in the light of their existing priorities.'
At present, the line runs from Shoreditch through Whitechapel to New Cross and New Cross Gate via Brunel's tunnel under the Thames.
The proposals include new stations at Bishopsgate (replacing Shoreditch), Hoxton, Haggerston and Dalston Junction and a new train servicing facility at Silwood in south-east London.
London Underground also hopes East London Line services will be extended via the North London Line to Highbury and Islington.