Yes, that's completely fine - in fact, lots of people here on the forum have done this because getting married in the US and then applying for a spousal visa, is often easier and cheaper than applying for a fiance visa, marrying in the UK and then applying for an FLR(M) visa.
There should be no problems with him getting into the US, as long as he can show immigration that he's not planning to live in the US after getting married (so paperwork he could bring might be a letter from his employer stating when he's due back at work, evidence of his housing in the US - rental agreement/mortgage statements etc.). There also shouldn't be any issue getting a marriage licence either.
If he wants to, he can print out this page on the US Embassy in London website stating that if foreigners wish to marry in the US but do not wish to live there, they should enter the US on the visa waiver program in order to marry (http://london.usembassy.gov/immigrant-visas/marriage-to-a-u.s.-citizen.html
If you will marry in the United States with the intention of taking up indefinite residence after marriage, you will require a fiancé(e) visa. For further information, please follow this link.
Note: If you will do not intend taking up indefinite residence in the United States but will continue to live and work abroad after the marriage ceremony you should apply for a B-2 visa, or if eligible travel visa free under the Visa Waiver Program.