Vue.js provides official support for TypeScript, and that support keeps getting better and better. The documentation for Vue.js's TypeScript support is located at https://vuejs.org/v2/guide/typescript.html.
The main npm package of Vue includes TypeScript type definitions (https://github.com/vuejs/vue/tree/dev/types), which is nice because those should stay well aligned with the project as it evolves.
At the time of writing, the latest release of Vue is 2.6, also known as Macross.
Vue 3.0, which should be released in 2019 (or early 2020), will feature full TypeScript support. Moreover, Vue.js itself will be written in TypeScript.