Tunnelling for the £1.2bn Northern Line extension will begin in March, Sadiq Khan has announced.
A pair of two-mile long tunnels, drilled by custom-built machines, will connect the Tube line to Battersea, south London.
New stations at Nine Elms and Battersea Power Station are due to open in 2020.
The extension, which will run west from Kennington, will be the first major expansion of the Tube since the Jubilee line in the late 1990s.
Named Helen and Amy, the two 650-tonne boring machines – built by NFM Technologies in Le Creusot, France – were unveiled earlier.
The 106m-long machines were named by local school children in honour of Helen Sharman, the first British astronaut, and British aviation pioneer Amy Johnson.
Each machine is capable of tunnelling up to 30 metres a day with teams of about 50 people needed to operate them.
The work is expected to take about six months to complete.
According to tunnelling tradition, the machines cannot start work until given a name.
Transport for London said the extension, funded entirely through contributions from the developments in the area, will support 25,000 new jobs and more than 20,000 new homes
Mayor of London Mr Khan said the extension would be “a real boost to south London”.
“I’m also delighted that local schoolchildren have chosen two such inspirational British women as the names for these tunnelling machines,” he added.