Yes, it's possible since I have done it… but I am not sure if there is any specific EU-wide rule or standard document for that and I am not able to provide anything more than an anecdote.
IIRC, I phoned my soon-to-be insurer (in the Netherlands) to ask if they would consider it and then sent some document provided by my previous insurer (not even sure if it was translated) and it somehow worked out. If my recollection is correct, it was simply the document you get when switching insurers within my previous country of residence, nothing more complex than that.
It might be useful to inquire before signing up. People don't switch between banks or insurers often so a new customer is always especially valuable for these businesses. I don't know how much leeway individual customer reps have but as someone who has just moved in and is willing to become a customer, you might have some leverage.