Jennifer, Joseph, Jillian and Jacob Crenshaw were returning from a family holiday to Disney World in Orlando, Florida, when the light plane they were travelling home in crashed.
Their plane took off from Kissimemee, Florida at 12:52 pm on Saturday, before the plane crashed around 2:30 pm over Alabama.
Jennifer, 43, Joseph, 45, and their two children, 16-year-old Jacob and 14-year-old Jillian, were killed in the crash.
"The relatives are grief stricken and in shock," the family said in a statement to ABC National News.
"They are a prominent family in Jackson Tennessee with roots that go back to the revolutionary war."