Yes ,You are eligible for SSC JE exam 2019.final year student are eligible for giving most of government services exam except few which demand full completion of the degree but SSC is not one of them.

To know more about SSC JE eligiblity follow this link to clear your minute doubt related eligibilty .Link:https://competition.careers360.com/articles/ssc-je-eligibility-criteria

Hope this helps you.