And like the Saturn rockets, it will be fuelled by safer liquid oxygen and hydrogen. The shuttle used solid boosters, which cannot be turned off once they have been ignited.
"It's back to the future with a reliable liquid technology," said Professor Scott Hubbard, a former Nasa official who investigated the 2003 space shuttle Columbia disaster.
The launcher will have a module design so the rockets of different sizes can be constructed to meet the demands of individual missions.
NASA SLS launch rocket
The rocket will be around 34 storeys tall
Unmanned test flights could start in 2017, with the first crew flying in 2021. A mission to a nearby asteroid could follow in 2025, and Mars in the 2030s.
Nasa administrator, and former astronaut, Charles Bolden said: "President Obama challenged us to be bold and dream big, and that's exactly what we are doing at Nasa.
"While I was proud to fly on the space shuttle, tomorrow's explorers will now dream of one day walking on Mars."
NASA SLS launch rocket
The plan is for the rocket to head to an asteroid in 2025
The new rocket programme is expected to cost US taxpayers $35bn (£22bn).
Since retiring the shuttle earlier this year, Nasa has commissioned commercial companies to design and operate cargo rockets to service the International Space Station.
It will concentrate its own resources on deep space exploration.