I do not trust electricians at all, so no, i am not sure he given me the right transformer. Therefore i ask you guys.
You didn't tell him what LEDs you want to use... He probably doesn't "trust" you either! ;)
That transformer is for 12V Halogen lights. It should work with 12V "LED bulbs" from the home improvement store. These LED bulbs are generally designed to replace incandescent-halogen bulbs the same way 120V/240V LED blubs are screw-in replacements for regular light bulbs. These LED light blubs have a built-in power supply. Some LED bulbs are dimmable and some are not. Most of them work on AC and some may work on DC.
That power supply is designed to be used with a regular in-wall dimmer on the high-voltage side.
It doesn't say if it puts-out AC or DC (and halogen bulbs work with either) but since it says 43kHz it's probably PWM DC. (Technically a "transformer" is AC and it's the main component in an AC or DC power supply. You can run a 12V halogen from a plain AC transformer)
If the power supply is DC it should work with a regular 12V LED strip from an electronic hobby supplier. If the power supply is AC you can use a full-wave rectifier between the transformer and regular DC LED strip.