"It's only a matter of time...Our Hamilton film. THIS July 3rd. On Disney+," Miranda -- the show's star and creator -- tweeted.
The post included an image of the blockbuster show's logo and a banner that said, "Experience the original Broadway production."
Miranda's wife Vanessa Nadal posted a photo of him wearing a Hamilton T-shirt and sitting in front of a laptop computer.
"Sneaky photo of @Lin_Manuel excitedly/nervously waiting to drop this news. He woke up like a jolt of energy (more than usual) and could not keep still!" she wrote.
Miranda followed up his original message with: "Never been so happy/nervous in my life.We all watching this together on July 3, yeah? #Hamilfilm."
Hamilton, which uses hip-hop music and a diverse cast to tell the story of the early days of American history, won 11 Tony Awards, including the top prize for Best Musical.
Cast members Leslie Odom Jr., Daveed Diggs and Renee Elise Goldsberg also won Tonys for their performances.
Miranda has had a good relationship with Disney in recent years, appearing in its live-action musical Mary Poppins Returns, and writing music and singing in its animated movie Moana.
News that Hamilton will soon be available as home entertainment arrived as Broadway and most other cultural institutions remain shut down due to social distancing practices enacted during the coronavirus pandemic.