The two products have now vanished from Apple's website and online store, with pages redirecting to Apple Music. Apple will continue selling the devices in stores until stocks run out.
Apple still offers the iPod Touch but, running on iOS, but this can be thought of as a four-inch iPad or a wi-fi iPhone, unlike Apple's original consumer devices.
"Today, we are simplifying our iPod lineup, with two models of iPod touch now with double the capacity starting at just £199, and we are discontinuing the iPod shuffle and iPod nano," Apple said in a statement to ZDNet.
Apple has also reduced the price of the iPod Touch 32GB and 128GB models to $199 and $299, respectively. In the UK, they're £199 and £299.
Apple introduced the first iPod Classic in 2001, shortly after the launch of iTunes, which became the iPod's music management software. It went on to become a popular consumer device that differed from Apple's traditional market in laptops and desktops.
The original iPod had a capacity of just 5GB but it was enough to store 1,000 songs. Later models increased to 30GB, allowing users to carry large catalogues navigate them easily with Apple's signature scroll wheel.
The iPod Classic was followed by the iPod Mini, which was replaced by the iPod Nano in 2005, offering a much thinner design than the original.
Announcing the Nano, Steve Jobs famously pulled one from his jeans coin pocket, billing it the biggest thing since the iPod Classic. It was 80 percent thinner than the Classic, yet still held 1,000 songs.
The iPod also played an important role in selling the iPhone with one of iOS 1.0's key features being the iPod app. Apple continued to call its main music app 'iPod' until iOS 5's release in 2011 and renamed it 'Music'. It retired the iPod Classic in 2014.