Frodo indeed sailed to the west and in the appendices to LOTR it's clear he arrived there. The reason he was allowed to was because he was one of the ring bearers (as Bilbo and Sam later).
Nothing else is said in the books, however, there is a Tolkien's letter that explains that Frodo's stay in Valinor (or Eressea) is for healing, but not for ever.
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