How to use vue-router's $route and $router properties with vue-class-component?

Question

I'm migrating my Vue 2 project from JS to TS with class-based components. In my code, I used vue-router by accessing this.$route and this.$router properties. However, in class-based Typescript components, accessing these properties obviously gives a compile-time error, because they are defined dynamically at runtime by VueRouter plugin.

// Something like this works fine in my JS-based Vue components
export default {
  methods: {
    route() {
      return this.$route;
    }
  }
}

// Compile time error: TS2339: Property '$route' does not exist on type 'RouteUser'.
@Component
export default class RouteUser extends Vue {
    route() {
      return this.$route;
    }
}

Then how do I use vue-router and vue-class-component together?