Universities are international places. Therefore any style or register of English which would be acceptable for an American university would also be fine to send to a European university. So called 'American English' is just as valid in Paris and Milan as it is in Washington. Nobody is going to worry whether you write 'centre' or 'center'.
In fact, you will find that US-style English is widespread throughout European academia, even in the UK. A personal observation: I work in Cambridge, where a large proportion of the students come from overseas. When I overhear non-native students talking, the dominant accent - whether the students come from China, Iran or Mexico - is actually an American accent.
But if that were not the case, you there would still be no need to make any changes to your letter. Formal/written English as written by an American is virtually identical to that written by a British or Australian person. Believe it or not, we use the same words, the same grammar and 99% of the same spellings as you do. In many cases, it is impossible to tell whether a business or academic-style letter has been written in so-called 'American' or 'British English'. There is no need to change anything in your letter.
Su.Ki. is (as usual) right. I live in Cambridge and also hear all those American accents.
Your letter won't need any changes. Color or colour, labor or labour, it's all the same.