object-fit: cover
will do exactly what you need.
But it might not work on IE/Edge. Follow as shown below to fix it with just CSS to work on all browsers.
The approach I took was to position the image inside the container with absolute and then place it right at the centre using the combination:
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
Once it is in the centre, I give to the image,
// For vertical blocks (i.e., where height is greater than width)
height: 100%;
width: auto;
// For Horizontal blocks (i.e., where width is greater than height)
height: auto;
width: 100%;
This makes the image get the effect of Object-fit:cover.
Here is a demonstration of the above logic.
https://jsfiddle.net/furqan_694/s3xLe1gp/
This logic works in all browsers.
Original Image

Vertically Cropped

Horizontally Cropped

Square Container
