It's always 'thanks' or 'thank you.' The above answers are a mixed bag. Most are incorrect. This is a common mistake that learners make.

You would normally just say "thank you" in a general sense, for example showing with gesture that you are talking, or you can turn to each one and say it individually if you like. "Thank you both for..." etc sounds very formal although it could be used and I don't think anyone would have a problem with this from a learner. Just bear in mind - "Thank you both" or "thanks to both of you" are both better than "thank you to both of you" (plus that's a mouthful) and "thanks both" which doesn't work.

As examples: Thank you both for... an unforgettable evening; everything that you have done;everything that you have done etc. Thank you, boys, thank both of you for saving my life... Thank both of you gentlemen... We would like... ...to thank both the FBI and the LVPD for... ...to thank both of them for... ...to thank both delegations for their initiative... ...to thank both Governments for their cooperation... ...to thank both you and your predecessor, Ambassador Luck, for... ...