You will need to get an export certificate of airworthiness for your aircraft which will make the process much easier to transition onto the EU register.
The most economical way to obtain one, is when you have your annual done
You will also have to either put the aircraft in a crate to get it over to the EU or alternatively install ferry tanks and have a ferry pilot fly it.
You will then have to stump up the EU vat at a rate dependant upon which EU country it is imported into.
On a lower value aircraft, it may be wise to consider selling your aircraft in the US and purchasing one over here that has already jumped through the hoops.