If you mean completely without bloodshed I don't happen to know any examples, though I'm sure it's happened.

If you mean without major armed conflict between the "conqueror" and the "conquered", there are many. For example, Rome annexed Egypt. There had been some combat between Egypt and Rome, but there wasn't major confrontation and concerted effort to conquer them from the start. Short version is Marc Antony had allied with Cleopatra after Julius Caesar's death, Octavian (who would become Augustus Caesar) beat him and deposed Cleopatra and formally annexed Egypt. But the natives weren't slaughtered en masse (though, of course, some were killed when Romans entered Egypt to deal with Marc Antony and Cleopatra, but mostly guards and soldiers) and there wasn't a major war between the countries as there when a country resists invaders and conquerers.

There are tons of other examples, I just thought I'd mention a famous one. Both Alexander the Great and Genghis Khan were known for conquering a people by destroying their armies but assimilating and merging their cultures.

The notion that you alluded to in your question seems in my experience a relatively common aspect of conquest in pre-modern world. with notable exceptions like the Roman conquests of Carthage and Corinth. Certainly it is an interesting aspect of both Seleukid and Arsakid practice to work relatively closely with conquered native populations.

Do you mean to suggest that the two sides had never interacted before?

It's a pretty grey area in truth, but European colonization of New Zealand can be seen as a primarily diplomatic effort, which ended with Maori entirely 'belonging' to the crown (in the same way that European citizens were).

The treaty of Waitangi was the major tool here, a legal document whereupon the crown and a group of Maori chieftains agreed to share New Zealand and respect one another's independence and authority.

The grey areas come in with the fact that not all Maori agreed to the treaty, and even those that agreed found that the two different translations of the treaty meant slightly different things. Maori and Europeans also found that their concepts of ownership were wildly different and not wholly compatible.

So there was some fighting, exploitation, and a touch of cultural genocide, but the Maori were always viewed (roughly) as equals by the law, were never enslaved, and their culture is still very much alive today.