The application of Information technology in educational context and environment has dramatically changed the pattern at which people teach and learn. Institutions of higher learning globally are increasingly adopting e-Assessment as a replacement for traditional pen on paper examination due to its cost effectiveness, improved reliability due to machine marking, accurate and timely assessment. In spite of the numerous benefits of e-assessment, it is unclear if University students in Sub Saharan African Countries are willing to accept it. The purpose of this study is to examine technical support role towards mitigating effects of computer anxiety on electronic assessment amongst University students in Nigeria and Cameroon. Therefore, the study extended Technology Acceptance Model and was validated using 102 responses collected randomly across universities in Nigeria and Cameroon. This study supports the body of knowledge by establishing that Computer Anxiety is an important factor which can affect University students regardless of their level of computer proficiency. The outcome of the proposed model indicated that when technical assistance is provided during e-Assessment, computer anxiety on majority of University students in Nigeria and Cameroon is reduced. The practical implication of this study is that students’ actual academic potentials may not be seen if education policy makers and University administrators do not always strive to ensure that all measures, including technical support that can reduce fear associated with use of computer for assessment, are introduced.