According to the Japanese Wikipedia, for the earliest light novels, artists were selected by the publishing company EITHER for their work in 油絵 (abura-e = oil painting) and 水彩画 (suisaiga = watercolor) OR for their work in manga-style art, such as PC games. In 1987, the 少女文学 (shoujo bungaku = girl's literature) or 少女小説 (shoujo shosetsu = girl's novels) genre began, and for the first time shoujo manga style was used, which helped set the trend of manga-style art as the standard for light novels from the 1990s.
According to 『ライトノベル「超」入門』 (Raito Noberu "Chou" Nyuumon = Ultra-Initiation to Light Novels) by 新城カズマ (Shinjou Kazuma）pages 105-116, the increasing demand for anime-style artists available for light novel illustrations grew so large that it was necessary to develop a system for the industry to produce a large number of illustrations in a short time period (this time demand was partly off-set by the introduction of illustration software, allowing artists to complete illustrations in a shorter time frame).
Currently, it is standard practice that each artist is associated with a particular publisher. This means that they can switch between manga and light novel magazines, but they only switch between magazines all owned by the same publisher. For example, Obana Miho is a mangaka under 株式会社集英社 (Kabushikigaisha Shuueisha), so her earlier works like 『こどものおもちゃ』 (Kodomo no Omocha = Children's Toy) and 『パートナー』 (Partner) were published in Shuueisha's 「りぼん」(Ribon) magazine, her 『ハニービター』 (Honey Bitter) is published in its 「Cookie」magazine, and her 『あるようでない男』(Aru You de Nai Otoko = Not That Kind of Guy) was published as a one-shot in its 『りぼんオリジナル』 (Ribon Original) magazine and then serialized in its 「コーラス」 (Chorus) magazine. Her novelizations of 『この手をはなさない』 (Kono Te wo Hanasanai = I Won't Let Go of This Hand) and 『こどものおもちゃ ガールズ バトルコメディ』(Kodomo no Omocha Girl's Battle Comedy) were published under Shuueisha's コバルト文庫 (Cobalt Bunko = Cobalt Library) line of light novels.
Thus, to select the artist for a light novel, any of the artists associated with that publishing house are fair game; it partly depends on how busy they are on other projects, what connotations their art is associated with, and their fanbase.
However, there are some rare exceptions to the rule. Takeuchi Naoko was associated with 株式会社講談社 (Kabushikigaisha Koudansha), which published her 『美少女戦士セーラームーン』 Bishoujo Senshi Sailor Moon = Pretty Guardian Sailor Moon) in 「なかよし」 (Nakayoshi) magazine and Codename ha Sailor V in its 「るんるん」 (RunRun) magazine. She illustrated all the light novels authored by Koizumi Marie up through the 『マーメイド・ぱにっく』 (Mermaid Panic) series: 『ま・り・あ 』(Maria), 『あたしのわがままを聞いて…』 (Atashi no Wagamama wo Kiite… = Listen to My Selfishness...), and 『絶対、彼を奪ってみせる! 』(Zettai, Kare wo Ubatte Miseru! = I'm Definitely Gonna Steal Him!). However, after Kodansha lost some pages of her 『PQ Angels』 manga manuscript before it made it into print in late 1997/early 1998, Takeuchi abadoned that series and was recruited by rival company Shuueisha, which published her Punch series in its 「Young You」 magazine in 1998. After Takeuchi left Kodansha, illustrations for Koizumi Marie's novels were assigned to Ogura Masora whose style is shoujo but otherwise not particularly-related to Takeuchi's. After publishing many Koizumi/Ogura novels, Koizumi's work was consistently illustrated by Kitagawa Miyuki, who is best known for her manga series 『あのこに1000%』 (Ano Ko ni 1000% = That Girl Goes to 1000%) and 『東京ジュリエット』 (Tokyo Juliet), then by Takada Tami, and Koizumi's most recent novels have been illustrated by a variety of artists. Five years after Takeuchi's departure from Kodansha, Takeuchi returned to Kodansha to publish her 『ラブ・ウィッチ』(Love Witch) manga.
Some light novel authors have the talent and skills to illustrate their own light novels (or, as the case may be, get accused of plagiarism for re-working other's artwork). Some light novels are self-published online and have no ties to publishing companies, so they are completely free to choose their illustrator.
『このライトノベルがすごい!』 (Kono Raito Noberu ga Sugoi! = This Light Novel is Amazing!) published annually in November and 『ライトノベル・データブック』 (Light Novel・Data Book) explain the history of light novels and project an overview of upcoming trends in the industry.