Bicycle disc brake rotors
As long as you existing rotors are in good condition and thicker than 1.6mm (minimum safe thickness) you should have no issue with using them with the Shimanos. There doesn't seem to be an industry standard specification for rotor thickness but it is generally taken to be between 1.8mm - 2.0mm. The new callipers will self adjust to the rotor width.

Clean your existing rotor up with some rubbing alcohol (or similar solvent which doesn't leave a residue) before installing the new brake system to ensure there's no contamination.