On these terms is a common phrase used to signify a particular agreement or understanding between two parties. Some synonyms that can be used in place of on these terms include according to these conditions, under these circumstances, pursuant to this agreement, in compliance with these rules, and through this arrangement. These synonyms can be used based on the context of the situation or agreement. Whether you are in a formal business agreement, contract or in a casual setting, knowing the various synonyms to use for on these terms will help in clear communication and understanding between whoever you are dealing with.