Firstly, it's really fortunate that you're moving from a country that drives on the right, like Tenerife, meaning your car is left-hand-drive.
Regarding matriculation to Spanish plates, there's a complicated process to go through. If you check out this website, it takes you through the whole process.
Also, there's a company that does it all for you and their website can be accessed here.
Jun 17, 2016 Rating
Not for the Canaries! by: Andy
The company mentioned as being able to do the paperwork for you does not do so for the Canary Islands !!! I contacted them and they replied..."I am very sorry but we do not deal with the Canary Islands, they have totally different legislation to main land Spain."