Either surface snapping that Modron mentioned or projecting with shrinkwrap.
Snapping:
[ATTACH=CONFIG]211313[/ATTACH]
Circle (10 vertices), aligned
Face snapping and option to snap on to another object enabled
In edit mode, move (g) all vertices and snap them on the curved object by holding down ctrl and pointing on the object
Shrinkwrap:
[ATTACH=CONFIG]211315[/ATTACH]
Apply circle rotation (ctrl+a) so that you get the correct axis in the modifier
Add shrinkwrap modifier, enable project option, project axis, positive and negative, and on which object it needs to wrap
Apply shrinkwrap modifier
Join the two objects in object mode (ctrl+J) and connect the edges in edit mode. Also, add perimeter loops near the hole edge.
[ATTACH=CONFIG]211316[/ATTACH]