"I will eat this tomorrow."
Translation:Я з'їм це завтра.
Aspects in Ukrainian (з'їм, буду їсти) and in English (will have eaten, will eat) do not really translate as one-to-one.
The difference between "з'їм" and "буду їсти" is in that the former contains extra information not only about the verb, but about the final state of the object (in this case, the food). "Я з'їм це" means "I will eat all of it, nothing will be left afterwards", while "Я їстиму це" lacks the information whether all the food is eaten or not, a general statement about eating in the future. Quite different form the usage of perfect and simple aspect in English (or for that matter, continuous).
So, "Я з'їм це завтра" can be translated as "I will eat it" or "I will have eaten it" (also "I will finish eating it"). And "Я їстиму це завтра" as "I will eat it" and "I will be eating it".