Alexander Zaytsev first published his observations regarding the products of elimination reactions in Justus Liebigs Annalen der Chemie in 1875. Although the paper contained some original research done by Zaytsevs students, it was largely a literature review and drew heavily upon previously published work. In it, Zaytsev proposed a purely empirical rule for predicting the favored regiochemistry in the dehydrohalogenation of alkyl iodides, though it turns out that the rule is applicable to a variety of other elimination reactions as well. While Zaytsevs paper was well referenced throughout the 20th century, it was not until the 1960s that textbooks began using the term "Zaytsev's rule".
Zaytsev was not the first chemist to publish the rule that now bears his name. Aleksandr Nikolaevich Popov published an empirical rule similar to Zaytsevs in 1872, and presented his findings at the University of Kazan in 1873. Zaytsev had cited Popovs 1872 paper in previous work and worked at the University of Kazan, and was thus probably aware of Popovs proposed rule. In spite of this, Zaytsevs 1875 Liebigs Annalen paper makes no mention of Popov's work.
Any discussion of Zaytsevs rule would be incomplete without mentioning Vladimir Vasilyevich Markovnikov. Zaytsev and Markovnikov both studied under Alexander Butlerov, taught at the University of Kazan during the same period, and were bitter rivals. Markovnikov, who published in 1870 what is now known as Markovnikovs rule, and Zaytsev held conflicting views regarding elimination reactions: the former believed that the least substituted alkene would be favored, whereas the latter felt the most substituted alkene would be the major product. Perhaps one of the main reasons Zaytsev began investigating elimination reactions was to disprove his rival. Zaytsev published his rule for elimination reactions just after Markovnikov published the first article in a three-part series in Comptes Rendus detailing his rule for addition reactions.