Please offer an data processing agreement and according data protection policies for your cloud service. EU customers are not allowed to use your product without this!
Additionally this could grant you access to the Privacy Shield list which is the reference for EU businesses to pick partners in the US.
@istinka is right, EU customers are not allowed to use your product without a data processing agreement which gives EU customers assurance of EU GDPR compliance.
I'm in the EU and would like to switch to cloud, but can't because of this very issue.
I know achieving compliance is never easily done, and can be a daunting task. On the other hand, the EU is a big market (just shy of 500 million folks, and not the poorest ones).
Some additional hints may be found here:
https://ec.europa.eu/info/law/law-topic/data-protection/international-dimension-data-protection_en
Of which the Standard Contractual Clauses (SCC) could seem to be of specific interest for your case (export of data outside the EU).
