"Today, A.C. Milan S.p.A. (AC Milan) and F.C. Internazionale Milano S.p.A. (FC Internazionale) filed with the Municipality of Milan the 'Technical and Economic Feasibility Study' for the new Milan stadium and its multifunctional district," the clubs said in a joint statement.
The proposal is the first step towards construction of a new ground adjacent to the current San Siro, while the old stadium will make way for an area "dedicated to sports, entertainment, and shopping".
The two clubs say that the project will require investment of 1.2 billion euros ($1.34 billion) and lead to jobs for 3,500 people.
Eventual approval from the city for the proposal filed on Wednesday would give a preliminary green light and mean Milan and Inter would then have to provide a "definitive plan" which would also have to be approved before any building could begin.
The proposal also said it was not possible to renovate the existing San Siro.
Milan president Paolo Scaroni and Inter CEO Alessandro Antonello had already announced last month the clubs' intention to knock the San Siro down, but have met resistance from the city's mayor Giuseppe Sala.
Sala said the current ground, which is owned by the city, would still be standing in 2026 as it was included in the victorious Milan-Cortina d'Ampezzo bid for that year's Winter Olympics as site of the opening ceremony.
Most clubs in Italy play in stadiums owned by local authorities, although that has been slowly changing in recent years.
Atalanta, who are in next season's Champions League after finishing ahead of the Milan clubs in May, are building a new ground on the site of the formerly city-owned Stadio Atleti Azzurri d'Italia.
Serie A rivals Roma are also trying to get a similar project in the south-west of the Italian capital built, but it has been stuck in a bureaucratic quagmire since being given initial 'public interest' approval in 2014.
Their project is complicated by the need to build infrastructure to serve the 52,500-capacity arena and disputes over the proposed adjacent business park.
Juventus, meanwhile, have won the Serie A title every season since their Allianz Stadium was opened in 2011. Their rebirth since relegation in the aftermath of the 'Calciopoli' match-fixing scandal has been helped by a marked increase in revenues from the redeveloped ground.