Update 2023
Here is what worked for me (finally):
ViteConfig:
import { fileURLToPath, URL } from "url";
import { defineConfig } from "vite";
import vue from "@vitejs/plugin-vue";
// https://vitejs.dev/config/
export default defineConfig({
  plugins: [vue()],
  resolve: {
    alias: [
      { find: '@', replacement: fileURLToPath(new URL('./src', import.meta.url)) },
      { find: '@assets', replacement: fileURLToPath(new URL('./src/shared/assets', import.meta.url)) },
      { find: '@cmp', replacement: fileURLToPath(new URL('./src/shared/cmp', import.meta.url)) },
      { find: '@stores', replacement: fileURLToPath(new URL('./src/shared/stores', import.meta.url)) },
      { find: '@use', replacement: fileURLToPath(new URL('./src/shared/use', import.meta.url)) },
    ],
  },
});
TSConfig:
{
  ...
  "compilerOptions": {
    ...
    "paths": {
      "@/*": ["./src/*"],
      "@assets/*": ["./src/shared/assets/*"],
      "@cmp/*": ["./src/shared/cmp/*"],
      "@stores/*": ["./src/shared/stores/*"],
      "@use/*": ["./src/shared/use/*"]
    }
  }
}
Update 2022
This solution comes by default from when creating a new project with npm init vue@latest
import { fileURLToPath, URL } from "url";
import { defineConfig } from "vite";
import vue from "@vitejs/plugin-vue";
// https://vitejs.dev/config/
export default defineConfig({
  plugins: [vue()],
  resolve: {
    alias: {
      "@": fileURLToPath(new URL("./src", import.meta.url)),
    },
  },
});
In components use @/:
<script setup>
import HelloWorld from "@/components/HelloWorld.vue";
</script>
This is what worked for me:
import path from 'path'
import { defineConfig } from 'vite'
import vue from '@vitejs/plugin-vue'
// https://vitejs.dev/config/
export default defineConfig({
  plugins: [vue()],
  resolve: {
    alias: {
      '@/': `${path.resolve(__dirname, 'src')}/`
    }
  }
})
Then in components:
<template>
  <img alt="Vue logo" src="./assets/logo.png" />
  <HelloWorld msg="Hello Vue 3 + Vite" />
</template>
<script>
import HelloWorld from '@/components/HelloWorld.vue'
export default {
  name: 'App',
  components: {
    HelloWorld
  }
}
</script>