That would be a Foley artist. Very cool job. Well, actually,
there are many people involved. A Foley artist is the person that
creates the sounds (e.g. claps the coconuts to make horse galloping
sounds). That's the fascinating part to me! They work with a
recording engineer who captures the sounds. There is also a person
who does the sound editing in a movie (the mixer, I think). That is
the person who decides what audio to use from the original shoot,
from the foley artist, from a sound effects database, overdubbed
with music, etc. etc. Technically that would be the person who
"puts them in" the movie.
interesting interview with a foley artist at
http://woodyssoundadvice.com/?p=22