I got my rings inspected yesterday, and the jeweler handed them back to me, engagement ring first, then wedding band, so I put them on in that order.
I usually wear my wedding band on the bottom, then engagement ring and decided to google last night the 'correct' way to wear them, & got conflicting results.

Thought it'd be interesting to see how most women wear them! Any specific reason why?

"The first option is to wear them on the traditional ring finger, on your left hand, in the order your received them in. This means the diamond ring goes on bottom, and the wedding band on top.
Keeping with tradition, you can wear both rings on the left hand on the ring finger, but with the engagement ring on top. This could be because you like it better, or because it simply looks better this way. There are those who do it for sentimental reasons as well. They feel that wearing the wedding band on the bottom keeps it closer to the heart."