Officials say the museum could open sometime in 2018 at a county park on eastern Long Island.
It will be named for Lt. Michael P. Murphy . The Medal of Honor recipient died along with 18 others in a gun battle in eastern Afghanistan in June 2005.
Their story was chronicled in the book and film, "Lone Survivor."
The museum would be the third honoring SEALs. The others are in Fort Pierce, Florida and Coronado, California.
New York state Sen. Thomas Croci (KROW'-chee) says a $400,000 state grant will help fund the project. The total cost is estimated at up to $4 million. A foundation named for Murphy will lead the fundraising project.