The decision was delayed after the 11 September terrorist attacks on New York, as home secretary David Blunkett was "too busy" reviewing security issues to approve the contracts.
The company will design and build the 450-place category B women's prison with Sheffield architect HLM. It will include 12 places for mothers with babies and 10 for women with mental health problems.
The first prisoners for the Ashford facility are expected to be admitted in July 2003.
The prison is one of a number undertaken by Interserve, a Reading-based company that was formerly known as Tilbury Douglas.
Interserve was also told last month that it had won a contract to provide a prison in Peterborough, Cambridgeshire.
It has built two other prisons as a member of the UK Detention Services consortium, which includes the French firm Sodhexo Alliance and Royal Bank Project Investments.
Interserve is in the process of building a £55m immigration detention centre near Heathrow, a deal that was announced at the beginning of the year.