The charities will work with support services company and consortium leader Serco to provide and run services at the prison at Belmarsh West, London.
Construction is due to start immediately and finish during the first half of 2012. The contract will run for 26 and a half years.
Both charities said their exact roles in the contract were not yet clear, but would likely involve the provision of prisoner resettlement services.
A spokeswoman for Turning Point said: "We understand this to be a groundbreaking project, with each member of the alliance bringing something different to the table.
"By combining our knowledge and experience, we plan to support well-run prisons that take positive steps towards reducing reoffending."
A Catch22 spokesman said that in order to reduce crime, resettlement services that delivered significant interventions were necessary.
The Charity Commission said earlier this year that it would look into the role of charities in running prisons.
The "fact-finding" mission was prompted by local umbrella body Navca and the Howard League for Penal Reform, which claimed that voluntary sector involvement in punishment contradicted the ethos of charity.
The Serco-led consortium was selected in June 2009 as the preferred bidder to build the new prison and one other at Maghull, Liverpool. The contract for the Liverpool jail is expected to be signed later this year.