Various families of quaternion and octonion number sequences (such as Fibonacci quaternion, Fibonacci octonion, and so on) have been established by a number of authors in many different ways. In addition, formulas and identities involving these number sequences have been presented. In this paper, we aim at establishing new classes of octonion numbers associated with the familiar Jacobsthal and Jacobsthal-Lucas numbers. We introduce the Jacobsthal octonions and the Jacobsthal-Lucas octonions and give some of their properties. We derive the relations between Jacobsthal octonions and Jacobsthal-Lucas octonions.