Epeus (or Epeius or Epeos), a skilled boxer (Iliad XXIII), is credited with building the Trojan horse with the help of Athena, as is told in the Odyssey IV.265ff and Odyssey VIII.492ff.
Pliny the Elder (according to "The Trojan Horse: Timeo Danaos et Dona ferentis," by Julian Ward Jones, Jr. The Classical Journal, Vol. 65, No. 6. March 1970, pp. 241-247.) says the horse was invented by Epeus.
However, in Vergil's Aeneid Book II, Laocoon warns the Trojans against the treachery of Odysseus which he sees behind the horse-gift of the Greeks. Incidentally, it's here that Laocoon says: timeo Danaos et dona ferentis 'Beware of Greeks bearing gifts.' In the Epitome of Apollodorus V.14, credit is given to Odysseus for conceiving the idea and Epeus for building:
By the advice of Ulysses, Epeus fashions the Wooden Horse, in which the leaders ensconce themselves.
There are other opinions on who devised the idea of the horse (with Athena's help) and what the horse really was, but whether Odysseus had the inspiration for the horse and/or figured out how to get the Trojans to take it into the city, Odysseus, tamer of the Trojans, is credited with using the horse to trick the horse-loving Trojans.