The Scottish Prison Service had planned to start building HMP Inverclyde this year but construction is now scheduled to start in 2014.
The new 300-cell jail will replace Scotland's only female prison, Cornton Vale near Stirling, and will house high risk and long-term female inmates from across the country.
The site in Inverkip Road in Greenock is currently home to St Columba's High School which is due to move to new premises.
Inverclyde Council, which leases the land from SPS, asked to stay on the site for an extra six months and this has been agreed.
HMP Inverclyde prison was originally planned as a replacement for Gateside Prison, also in Greenock, but Justice Secretary Kenny MacAskill said the alternative use was part of a major shake-up in the way female prisoners are treated.
SPS says that this means that Gateside jail could be retained, making Greenock a two-prison town.
There is currently space for 50 female inmates at Gateside Prison.
Scottish Government's Commission on Women Offenders stated that the female prison population in Scotland has doubled in the past 10 years.
It recommended that Cornton Vale be replaced with a specialist prison for those women offenders serving a statutory defined long term sentence and those who present a significant risk to the public.
A spokeswoman for the SPS said: "Inverclyde Council had an option to extend its lease at the site, and have notified us that they require to exercise that extension until January 2014.
"We are happy to accommodate that.
"Construction of the new HMP Inverclyde will commence when the lease has expired."
A spokesman for Inverclyde Council said: "We have exercised a clause in our agreement, which was open to us, giving the option to extend our lease on the site.
"We now plan to vacate the site in 2014."