Edit in JSFiddle

<div class="container">
  <div class="box">
    <p>Text for the box
    </p>
    <div class="button">
      <a href="#">Click Me</a>
    </div>
  </div>
  <div class="box">
    <p>Text for the box
      <br> More Text in this box
    </p>
    <div class="button">
      <a href="#">Click Me</a>
    </div>
  </div>
</div>

.container {
  display: flex;
  text-align: center;
  font-family: 'arial';
}

.box {
  display: flex;
  flex-flow: column nowrap;
  margin: 20px;
  padding: 10px;
  background: #ccc;
}

.button {
  margin-top: auto;
  padding: 5px;
  background: #555;
}

.button a {
  color: #fff;
  text-decoration: none;
}