 He is a former chief executive officer (CEO) of both Encyclopædia Britannica Inc. and Britannica.com Inc.. On 16 May 2001, he replaced Don Yannias in the latter position.When Britannica.com Inc. was spun off from Encyclopædia Britannica Inc. in 1999 to develop the "Britannica's" digital versions, Yannias switched to being CEO of Britannica.com Inc., leaving the CEO-ship of Encyclopædia Britannica Inc. vacant.The two CEO-ships were re-united under Yeshua, who had been serving as CEO of Britannica Israel, Ltd., a wholly owned subsidiary of Britannica.com Inc.

Before his time with the "Britannica", Yeshua was long associated with the Centre for Educational Technology (CET), an educational technology firm based in Tel Aviv that was partially acquired by Britannica.com Inc. At CET, he worked his way up through several positions, including marketing manager, head of the medical division and developer of educational learning materials, and finally deputy general director.