Three "super-prisons" each housing about 2,500 offenders are to be built, Justice Secretary Jack Straw has said.
Following a review of overcrowding in jails, he said a building programme would take prison place numbers up to 96,000 from the current 81,000 by 2014.
Plans to build 9,500 of these places had been announced previously.
Ministers would look at recommendations that sentencing in England and Wales should be more closely linked to the number of jail places, Mr Straw said.
The report, by Labour peer Lord Carter of Coles, looked at the prison system and the supply and demand of prison places.
Mr Straw told the Commons one of the proposals to set up a Sentencing Commission, which will be considered by ministers, had "nothing to do with linking individual sentences to the availability of correctional resources".
Instead, the commission would look at the overall sentencing framework in relation to the prison population, he said.
The building programme, part of Lord Carter's recommendations, would cost an extra £1.2bn on top of the current £1.5bn, Mr Straw said.
One of the so-called Titan jails, which will be larger than any prison currently used in Britain, will be in service by 2012.
The other two are expected to be built by 2014.
He suggested they should be built in London, the West Midlands and the north-west of England.
Mr Straw said: "The extra capacity will help to modernise the prison estate, close some of the older inefficient prisons on a new-for-old basis, reconfigure some of the smaller sites to accommodate female or juvenile offenders."
He added that short and medium-term measures to increase capacity included converting a former Ministry of Defence site at Coltishall in Norfolk into a Category C prison and HMP Wealstun near Leeds into a closed prison.
The Ministry of Justice was also looking into the possibility of a prison ship, he said.
Mr Straw added that the Criminal Justice and Immigration Bill would be amended to introduce a minimum tariff of two years, below which indeterminate sentences of Imprisonment for Public Protection (IPP) could not be given.
This would mean only the most serious and dangerous offenders would be given IPPs, he said.
"The measures I have announced today... will bring many more prison places on stream with agreed funding and a delivery programme," he said.
"They will allow for a rational debate on sentencing which recognises that, as with any other public service, resources are finite.
"And, above all, they will fulfil our commitment to provide a modernised prison system that protects the public from the most serious offenders," said Mr Straw.
However, shadow justice minister Nick Herbert called Lord Carter's recommendations a "devastating indictment" of the government's failure to manage the prison system.
Former Justice Secretary Lord Falconer had tasked Lord Carter with investigating the supply of prison places and demand for them in the short, medium and longer term.
Lord Carter consulted the Lord Chief Justice of England and Wales, Lord Phillips, who has also suggested linking resources to the setting of the sentencing framework.
The latest prison population figure for England and Wales show it has dropped to 81,455 from a record high earlier in November.
The Ministry of Justice says that, since Labour came to power in 1997, there are 20,000 more prison places - 3,100 of which were built in the last two years.