To marry a foreigner in the UK you usually need a Certificate of Approval (CoA), which basically states that the law of his home country has no reason to prevent the marriage. Since the USA do not have a marriage register, this is usually done by signing an affidavit at a US consulate.

Now because you do not live in the UK, you cannot apply for a CoA directly. Instead, he can apply for a visitor-for-marriage visa at the British consulate, which serves as a CoA. Once you are in the UK, you need to go to a designated register office (because only very few deal with foreign marriages), and give at least 15 days notice.