diff --git a/fastapi/applications.py b/fastapi/applications.py
index 6d427cdc2..2d9944c99 100644
--- a/fastapi/applications.py
+++ b/fastapi/applications.py
@@ -1050,7 +1050,21 @@ class FastAPI(Starlette):
 
     async def __call__(self, scope: Scope, receive: Receive, send: Send) -> None:
         if self.root_path:
+            root_path = scope.get("root_path", "")
+            if root_path and self.root_path != root_path:
+                logger.warning(
+                    f"The ASGI server is using a different root path than the one "
+                    f"configured in FastAPI. The configured root path is: "
+                    f"{self.root_path}, the ASGI server root path is: {root_path}. "
+                    f"The former will be used."
+                )
             scope["root_path"] = self.root_path
+            path = scope.get("path")
+            if path and not path.startswith(self.root_path):
+                scope["path"] = self.root_path + path
+            raw_path: bytes | None = scope.get("raw_path")
+            if raw_path and not raw_path.startswith(self.root_path.encode()):
+                scope["raw_path"] = self.root_path.encode() + raw_path
         await super().__call__(scope, receive, send)
 
     def add_api_route(
diff --git a/tests/test_root_path_redirects.py b/tests/test_root_path_redirects.py
new file mode 100644
index 000000000..150693b34
--- /dev/null
+++ b/tests/test_root_path_redirects.py
@@ -0,0 +1,52 @@
+from fastapi import APIRouter, FastAPI
+from fastapi.testclient import TestClient
+
+
+def test_redirects_without_root_path():
+    app = FastAPI()
+    router = APIRouter()
+
+    @router.get("/hello/")
+    def hello_page() -> str:
+        return "Hello, World!"  # pragma: nocover
+
+    app.include_router(router)
+
+    client = TestClient(app, base_url="http://testserver")
+
+    response = client.get("/hello", follow_redirects=False)
+    assert response.status_code == 307
+    assert response.headers["location"] == "http://testserver/hello/"
+
+
+def test_redirects_with_root_path():
+    app = FastAPI(root_path="/api")
+    router = APIRouter()
+
+    @router.get("/hello/")
+    def hello_page() -> str:
+        return "Hello, World!"  # pragma: nocover
+
+    app.include_router(router)
+
+    client = TestClient(app, base_url="http://testserver")
+
+    response = client.get("/hello", follow_redirects=False)
+    assert response.status_code == 307
+    assert response.headers["location"] == "http://testserver/api/hello/"
+
+
+def test_invalid_combination_of_root_path():
+    app = FastAPI(root_path="/api")
+    router = APIRouter()
+
+    @router.get("/hello/")
+    def hello_page() -> str:
+        return "Hello, World!"  # pragma: nocover
+
+    app.include_router(router)
+
+    client = TestClient(app, base_url="http://testserver", root_path="/notapi")
+    response = client.get("/hello", follow_redirects=False)
+    assert response.status_code == 307
+    assert response.headers["location"] == "http://testserver/api/hello/"