Full Definition of RIVET. transitive verb. 1. : to fasten with or as if with rivets. 2. : to upset the end or point of (as a metallic pin, rod, or bolt) by beating or pressing so as to form a head. 3.4. : to attract and hold (as the attention) completely. — riv·et·er noun.ull Definition of RIVET. transitive verb. 1. : to fasten with or as if with rivets. 2. : to upset the end or point of (as a metallic pin, rod, or bolt) by beating or pressing so as to form a head. 3. 4.