I wrestled with this for a while so I figured I'd share it. It's a TypeScript implementation of the example "auth workflow" from the React Router docs, it's effectively the same concept just spiced up with types and it's embedded into a class so it can access app state easily.

react-router-auth-workflow-typescript.tsx

class App extends React.Component<{}, AppState> {

    // IfLoggedIn is a TypeScript version of:
    // https://reacttraining.com/react-router/web/example/auth-workflow
    // it's just a stateless component that takes path and component (similar to <Route>)
    // and renders the component if the user is logged in, if not, it redirects to /login
    IfLoggedIn = (thisProps: { path: string; component: Function }) => {
        return (
            <Route
                render={props =>
                    this.state.loggedIn ? (
                        thisProps.component
                    ) : (
                        <Redirect
                            to={{
                                pathname: "/login",
                                state: { from: props.location }
                            }}
                        />
                    )}
            />
        );
    };

    render() {
        return (
            <Router>
                <this.IfLoggedIn
                    path="/upload"
                    component={Upload}
                />
            </Router>)
    }
}