1
general::
You can be sure, as in Rest assured that the police will recover your diamonds. This expression uses assured in the sense of "certain" or "confident," a usage dating from the early 1500s.
American Heritage Idioms
2
general::
Phrase(s): rest assured
to be assured; to be certain. • Rest assured that you’ll receive the best of care. • Please rest assured that we will do everything possible to help.
McGrawhill's American Idioms And Phrasal Verbs