Connection device (100) for connecting a contact rolling bearing (1) to an external body (7), the connection device (100) presenting a peripheral connecting outline (5), which is obtained around a race (3) of the contact rolling bearing, and a complementary connecting outline (6), which is obtained inside the external body (7), and which presents a shape such as to complement the connecting peripheral outline (5) in order to render angularly integral in relation to each other the external body (7) and the first race (3), the connecting peripheral outline (5) and the complementary connecting outline (6) both presenting a radius (R) which is of variable angular dimensions with continuity on a plane which is transverse to the rotation axis (A), and are both provided, in relation to the rotation axis A, with at least one respective convex portion (51).