Yes they sure can be! Just make sure it's compatible with the new mobo you want to install it in. If you're not sure, give us the exact CPU (example: i7-7700k or Ryzen 7 2700X) and a resident guru here will be able to steer you in the right direction as to which mobo to buy. Sometimes, you'll get even better performance if you install the CPU into a different mobo. As in it may have better on-board audio or more RAM can be installed.
What you're looking for is a Micro-ATX motherboard for a socket 1155 CPU. It needs to have any of the following Intel chip sets: H61, Z68, B75, H77, Z77. Given the age of these motherboards, you're probably going to want to check used sites.