This compound word is simply the imperative phrase “fare well” treated as one word.  The OED classes it as poetical, so I will add our poetry tag to it.  It’s a lovely, high-sounding word for formal leavetakings.

• 03.050 Now they rode away amid songs of farewell
• 07.002 The dwarves were crying farewells
• 07.007 Farewell!’ they cried,
• 07.012 farewell wherever you fare!’
• 07.129 and bidding him many farewells they rode off
• 07.146 Now Gandalf too said farewell.
• 10.045 and his councillors bade them farewell
• 16.046 and then he said farewell to the elves
• 17.027 Farewell!’
• 17.029 in the meanwhile farewell!’
• 18.017 ‘Farewell, good thief,’
• 18.018 ‘Farewell, King under the Mountain!’
• 18.019 Farewell!’ (Thorin to Bilbo)
• 18.038 ‘Farewell, Balin!’
• 18.038 and farewell, Dwalin;
• 18.038 and farewell Dori, Nori, Ori,
• 18.038 Farewell Thorin Oakenshield!
• 18.044 Farewell! O Elvenking!’
• 18.045 Farewell! O Gandalf!’
• 18.049 Farewell!’ (Thranduil to Bilbo)
• 19.018 he said farewell to Elrond,

“farewell, int., n. (and adj.), and adv.” OED Online. Oxford University Press, March 2015. Web. 11 May 2015.