How to annotate variadic parameters in Python using typing annotations?

tl;dr

Basically args treated as a homogeneous tuple and kwds as a dictionary. You simply annotate a type being expected for each element value.

Explanation

Explanation arrives from quote of the PEP-484:

In the body of function foo, the type of variable args is deduced as Tuple[str, ...] and the type of variable kwds is Dict[str, int].

So there is no need to annotate args as whole homogeneous typed tuple but one can reduce Tuple[T, ...] to just type T.

Same true for the keyword arguments as they deduced as Dict[str, T]

About ellipsis in the tuple annotation

In python documentation there is no much information about the usage of the ... a.k.a Ellipsis but PEP-484 does mention various usages of the ellipsis in typing annotations like for omitting some type annotations or default values but most interestingly there is a qoute saying:

Tuple, used by listing the element types, for example Tuple[int, int, str]. The empty tuple can be typed as Tuple[()]. Arbitrary-length homogeneous tuples can be expressed using one type and ellipsis, for example Tuple[int, ...]. (The ... here are part of the syntax, a literal ellipsis.)

So if you omit asterisk to force passing arguments as a single tuple you need keep full annotation:

def foo(args: Tuple[T, ...]):
    ...

About various types in a homogeneous tuple

Since homogeneous tuple means all of its elements must be of the same type then if you wish to allow several types just use a Union or even use a type alias for better readability:

MyArg = Union[int, str, bool]

def foo(*args: MyArg):
    ...

If each argument has a TheType type - annotate it as specified in PEP-484:

def foo(*args: TheType):
    ...

Do not use: def foo(*args: Tuple[TheType]):, because specifying Tuple[TheType] means it's a single-element tuple - with one TheType element, which is not what variadic args are intended to serve.