You can just implement a user-defined type like the following:
type Nullable<T> = T | undefined | null;
var foo: Nullable<number> = 10; // ok
var bar: Nullable<number> = true; // type 'true' is not assignable to type 'Nullable<number>'
var baz: Nullable<number> = null; // ok
var arr1: Nullable<Array<number>> = [1,2]; // ok
var obj: Nullable<Object> = {}; // ok
// Type 'number[]' is not assignable to type 'string[]'.
// Type 'number' is not assignable to type 'string'
var arr2: Nullable<Array<string>> = [1,2];