This works fine as long as the analog video and power cable can be run to the cameras location from the DVR.
Cat5, 5E, 6, and 7 wire can also be used with a low-cost POE (Power over Ethernet) adapter that is quick and easy to setup.
The adapter also called an Inline Power Injectors simply convert the signal inputs to transfer over Ethernet and reconvert them on the other side.
POE Adapter on Amazon
Cable Matters Inline Passive Power Injector over Ethernet
There are several brands available all which are very low-cost easy to setup adapters.
One side will need the power supply plugged in which will transfer power over the Ethernet wire.
There is male and female connectors so the other side will have the right power plug input when needed.
Be sure to check the voltage on the cameras systems power supply you are using and match it to the inline adapter.
Most will be rated 5-12 Volts DC and 1 AMP, it is best to double check and be sure the cable can handle the voltage.
Passive POE can usually operate up to 100-130 feet.
Converting an old BNC style camera system to work over Ethernet is easy to do with a low cost adapter.
If you have the time and a soldering iron home kits can also be built.
The POE converting cables are so low-cost it likely is not worth the time and energy build it yourself but it is an option.
The cables shown above only convert the plugs to carry a signal over an Ethernet wire and convert is back. A power adapter will still be needed on one end to send voltage down the line.
As always be sure to read the reviews on Amazon, forums, or elsewhere to be sure a unit is a good fit for you.