package.json

{
  "name": "WebpackExample01",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1",
    "build": "webpack"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "devDependencies": {
    "@types/jquery": "^3.2.12",
    "@types/knockout": "^3.4.45",
    "jquery": "^3.2.1",
    "knockout": "^3.4.2",
    "ts-loader": "^2.3.7",
    "typescript": "^2.5.2",
    "webpack": "^3.5.6"
  }
}

steps.txt

execute following commands in a terminal:
  npm init -y
  npm install npm@latest
  npm install webpack --save-dev
  npm install --save-dev typescript ts-loader
  npm install --save-dev jquery @types/jquery

add pre-build event in visual studio project properties:
  npm run build

add "build" task to "scripts" section of package.json:
  "build": "webpack"

tsconfig.json

{
  "compilerOptions": {
    "noImplicitAny": false,
    "noEmitOnError": true,
    "removeComments": false,
    "sourceMap": true,
    "target": "es6",
    "module": "commonjs",
    "moduleResolution": "node"
  },
  "exclude": [
    "node_modules",
    "wwwroot"
  ]
}

webpack.config.js

var path = require('path');
var webpack = require("webpack");

module.exports = {
    entry: {
        app: ['./Scripts/app.ts'],
        vendor: ["jquery", "knockout"]
    },
    output: {
        filename: 'bundle.js',
        path: path.resolve(__dirname, 'wwwroot/dist/')
    },
    plugins: [
        new webpack.optimize.CommonsChunkPlugin({ name: "vendor", filename: "vendor.bundle.js", minChunks: Infinity })
    ],
    module: {
        rules: [
            {
                test: /\.tsx?$/,
                loader: 'ts-loader',
                exclude: /node_modules/
            }
        ]
    },
    resolve: {
        extensions: [".tsx", ".ts", ".js"]
    }
};