The design was presented in Milan on Thursday by renowned architect Norman Foster and stadium specialist David Manica, who have worked together on the project.
Foster described a structure that will remain relatively low in the centre before rising behind the goals, while the steeply positioned stands are designed to bring supporters closer to the action.
Manica said the project was built around the atmosphere that has made San Siro one of European football's most famous venues.
"The most important thing that we realised when we designed this project is that the San Siro is a feeling," he said.
"It's more than a building, it's a feeling, and everything that we needed to do here was to carry it into the (new) building."
The stands behind the goals will have a 37-degree incline, while the roof will cover the seating areas and help amplify the noise generated by supporters.
"We brought all the seats as close as possible to the field. They could not be any closer; it'll actually feel as though you're sitting on the grass," Manica added.
He also wants the stadium to recreate the intensity of the existing venue, saying he hopes supporters will feel the building "living and breathing with them".
The new stadium, which will also host American football, rugby and concerts, is expected to cost 1.2 billion euros, with construction scheduled to begin in 2028.
Inter and AC Milan paid 197 million euros to acquire the existing San Siro and surrounding parking areas, where their new home will be built. The current stadium, which opened in 1926 and has a capacity of 75,000, will be largely demolished once construction approaches completion.