Edit in JSFiddle

<input type="url" id="url">
<button id="getImageFromURL">get</button>
<div>
  <figure id="output"></figure>
  <p id="base64"></p>
</div>

#output {
  width: 200px;
  height: 200px;
  background-repeat: no-repeat;
  background-size: contain;
}

const output = document.getElementById('output');
const base64 = document.getElementById('base64');

document.getElementById('getImageFromURL').addEventListener('click', () => {
	const url = document.getElementById('url').value;

	const image = new Image();
  image.src = url;
  
  // CORSが許可されていない場合はエラーになる
  // [Tainted canvases may not be exported.]のエラー対策
  image.crossOrigin = 'anonymous';

  image.onload = () => {
    const canvas = document.createElement('canvas');
    canvas.width = image.width;
    canvas.height = image.height;
    canvas.getContext('2d').drawImage(image, 0, 0);
    
    const src = canvas.toDataURL('image/png');
    output.style.backgroundImage = `url(${src})`;
    base64.innerText = src;
  };
  
  image.onerror = e => {
  	console.log(e);
  	base64.innerText = '読み込みに失敗しました';
  };
});