If the wiring matches, you can simply use butt splices to pinch the wires together because 1. its easy and 2. the name. The pro move would be to use heat shrink types that you can seal after, but if this is just a hack job for passing inspection you could even do like my car's previous owner and twist the wires together and maybe even use electrical tape for style points, but I'm not a fan of that myself.

One thing to be wary of is that LED turn signals will draw a lower wattage then the incandescent, and so the flasher module will think the light is out and do hyperflash. Slightly annoying and often comical on other cars, I don't know if that is sufficient for passing.