I joined a new company as a web designer. My first task is to design a new template for my company website that follows the legacy of its older versions.

There is a problem. Our company website has had multiple versions over the past sixteen years.

Is there any tool to check the older versions of my company website?

You can check older designs and looks of a website with the help of Wayback Machine. This tool is also called Internet Archive. Visit the link below and type the URL of the website.
Click the Browse History button. It will show you the older captured photos of that website's older versions.

Web Achive is a very helpful tool.

It is a very good tool. Thank you for sharing.

WebCite is another tool to check for archived web pages. We can search for a website or ULR from their database with the exact date range.

Visit the following link to open WebCite and search for the older web content by providing the URL.