以vue-cli生成的项目为例

1.static文件夹下先放入ueditor文件

2.index.html添加如下代码

<script type="text/javascript" charset="utf-8" src="static/ueditor/ueditor.config.js"></script>
<script type="text/javascript" charset="utf-8" src="static/ueditor/ueditor.all.min.js"></script>

3.webpack.base.conf.js添加如下配置

externals: {
    'UE': 'UE',
  },

4.index.html中添加

<script type="text/javascript">
  window.UEDITOR_HOME_URL = "/static/ueditor/";//配置路径设定为UEditor所放的位置
</script>

5.editor组件

<template>
  <div>
    <mt-button @click="geteditor()" type="danger">获取</mt-button>
    <script id="editor" type="text/plain" style="width:1024px;height:500px;"></script>
  </div>
</template>

<script>
const UE = require('UE');// eslint-disable-line

export default {
  name: 'editorView',
  data: () => (
    {
      editor: null,
    }
  ),
  methods: {
    geteditor() {
      console.log(this.editor.getContent());
    },
  },
  mounted() {
    this.editor = UE.getEditor('editor');
  },
  destroyed() {
    this.editor.destroy();
  },
};
</script>

<style>

</style>

2018.6.29更新

评论中已出vue-ueditor-wrap，大家可以看下这个:
vue-ueditor-wrap