If you encounter the clue “crossword puzzle fan (14 letters)”, then cruciverbalist is the answer, though the word is as much used for the compiler crossword puzzles as the solver.
It seems to have appeared in English about 1980 (the first reference I can find is to the Compleat Cruciverbalist of 1981 by Stan Kurzban and Mel Rosen, subtitled “how to solve, compose and sell crossword puzzles for fun and profit”). However, Stan Kurzban tells me that Mel Rosen had encountered the word some years earlier in the title of a directory of crossword puzzle notables that was not widely circulated.
Whatever its origin, cruciverbalist has spread into the wider language as a result of their efforts to the extent that it now appears in some larger recent US dictionaries. The word is a modern mock-Latin invention, being a translation back into Latin of the English crossword (using Latin crucis, cross, as in words like cruciform, plus verbum, word, as in verbose or verbatim).
There is also cruciverbalism, for the art of crossword compilation or crossword fandom generally, but that is much rarer.