The Jubilee Line opened in 1979, and is London's newest Underground line in the sense that it was the last to be built. But this question is rather ambiguous, as other lines have officially joined the Underground network more recently.
The Hammersmith and City Railway opened in 1864 as a feeder to the Metropolitan Railway, of which it was considered to be a part. In 1988, however, it gained independence to become the Hammersmith & City Line in its own right.
The Waterloo & City Line (affectionately – or not – known as 'the Drain') opened in 1868 to become London's second underground railway, after the Metropolitan. After World War II it was run by British Railways, but in 1994 it became the Underground's 12th line.
This information comes from Transport for London's website.
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