Is it possible to put a 1.8 TDCi engine from a mk3 mondeo into a 2009 mk4 mondeo? Im looking to buy the 2009 one but needs a new engine 

What engine is in the mk4?

1.8 TDCi as well

Physically it's possible but the electrics may be the sticking point, I don't know how different they are

It is very probably possible but the amount of aggro involved could be anywhere from hardly any to almost infinite. This is quite a range.

If you can get the two wiring diagrams and trace them through to ensure that the same (nominal) connections were made that would be a good start. But you only have to run in to something like an air con module which has an output that works differently and you could have a car that stalls every time that you change gear with the air con on.  And it could be all sorts of other things apart from a/c.

Now having done that to make it legal for the road you have to get type approval. Here there will be a much more thorough test than an MoT. Now you could argue that with a relatively simple change like this it ought not to be too bad but  don't know of any route that gets you a simpler test.

And then there is insurance but that will need the approval and once you've got that they should only charge you money... 
 

An engine swap doesn't require type approval, that is only for radically modified vehicles

I thought that was only if you still had an engine approved to the same emissions standards, which this wouldn't be. They ought to check the engine code on an MoT, although possibly in practice they don't.
 

Dont know if this is relevant, but when I put a second hand engine in my focus it was the 1.8tdci from a mk2 not a mk2.5 and there are some differences between the two, this is what ford told me, and still ran. Also I highly recommend on changing the camblet on the 1.8 before you start it, they are prone to snapping, or in my case, the teeth shredding. 

 

Good Luck!