Usage of "to both of whom"

I am writing a short formal acknowledgement in a paper, and I would like to thank two people at the same time. The phrase I'm using is essentially:

Coffee was paid for by John and Anna, to both of whom I express my sincere gratitude.

I am not sure if the expression "to both of whom" is correct. Should it be "to whom both"? Maybe a small variation of the phrasing would work, but I can't think of any that is short and formal.

Answer

Coffee was paid for by John and Anna, to both of whom I express my
sincere gratitude.

is the correct of the two sentences you pose.

both OED

With a plural pronoun (denoting the members of a pair).
Immediately following (or in early use preceding) a subject or object
pronoun. Also in both which. Cf. sense C. 3, and both of us, both of
whom, etc., at sense

To use to whom both in your sentence:

Coffee was paid for by John and Anna, to whom both I and my companion
express sincere gratitude.