diff --git a/fastapi/applications.py b/fastapi/applications.py
index 6db4b4e83..7379d92eb 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -333,7 +333,7 @@ class FastAPI(Starlette):
             ),
         ] = None,
         dependencies: Annotated[
-            Optional[Sequence[Depends]],
+            Optional[Sequence[Depends | Any]],
             Doc(
                 """
                 A list of global dependencies, they will be applied to each
@@ -345,11 +345,12 @@ class FastAPI(Starlette):
                 **Example**
 
                 ```python
+                from typing import Annotated
                 from fastapi import Depends, FastAPI
 
                 from .dependencies import func_dep_1, func_dep_2
-
-                app = FastAPI(dependencies=[Depends(func_dep_1), Depends(func_dep_2)])
+                annotated_dep=Annotated[str,lambda:"annotated"]
+                app = FastAPI(dependencies=[Depends(func_dep_1), Depends(func_dep_2),annotated_dep])
                 ```
                 """
             ),
diff --git a/fastapi/routing.py b/fastapi/routing.py
index 907511081..47b9240f6 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -671,7 +671,7 @@ class APIRoute(routing.Route):
         return match, child_scope
 
 
-def get_api_router_dep(dep: params.Depends | Any) -> params.Depends:
+def get_depends_from_annotated(dep: params.Depends | Any) -> params.Depends:
     if isinstance(dep, params.Depends):
         return dep
     d = analyze_param(
@@ -948,7 +948,9 @@ class APIRouter(routing.Router):
             )
         self.prefix = prefix
         self.tags: List[Union[str, Enum]] = tags or []
-        self.dependencies = [get_api_router_dep(dep) for dep in dependencies or []]
+        self.dependencies = [
+            get_depends_from_annotated(dep) for dep in dependencies or []
+        ]
         self.deprecated = deprecated
         self.include_in_schema = include_in_schema
         self.responses = responses or {}