Is it possible to get a legal business agreement that is binding in the U.K. and U.S.

Yes, you can have a legal contract that is binding in both countries. You must choose one venue for disputes (i.e. which court you will use) and one country for application of law. Many people decide to use arbitration for international disputes as well.

I agree with the previous poster, but would like to add that contract drafting is not that simple. There are many other things you need to consider and should include, i.e. attorneys' fees, confidentiality, termination terms, etc. I do not understand if you would like to set up a business here in the US or in the UK, but you should know that your partner could be owner of a US business, he doesn't need to be a US resident.

I noticed that you stated you all are forming a business. If you are forming a business in the US, there are several aspects that you want to evaluate including entity type, taxation, etc. Please keep in mind that certain entity types in the US have restrictions with regard to who is allowed to be a shareholder. If you are considering a S-Corp, then your partner would not be allowed to be a shareholder if he is a UK citizen. As the other posters stated, there are ways that the contract can be drafted in order to be enforceable in both countries. Be certain to seek an attorney's advice prior to executing any agreements.