score:3
I have arrived in Sweden and can now answer my own question.
Even though I had insurance from my employer, I did not have any supporting documents. So I bought a 60 day travel-cum-medical insurance for me and my wife. We crossed the border control without any problems. The border guard did not ask anything.
To sum up, even though its mandatory to have an insurance when travelling to EU, in practice border guards rarely ask for proof. Anyway, having insurance is always a good idea. If not long term, choose a limited period insurance which will cover you till you get settled in the new place.
Upvote:1
All EU residents, including non-EU nationals working in EU are obliged to be insured in public health insurance systems. Systems vary between each EU country, but what does not vary is that it's mandatory.
While traveling within EU, the document required as proof of insurance is European Health Insurance Card. These cards are provided for free, all you need to do is apply to get one.
It wasn't obvious from the question, but you've clarified that you were traveling from outside of EU to country where you're going to be resident. I wouldn't expect requirement for travel insurance, which is required for short stays. On the other hand becoming legal resident you fall under public health insurance scheme.