Materials based on metallic elements that have d orbitals and exhibit room temperature magnetism have been known for centuries and applied in a huge range of technologies. Development of room temperature carbon magnets containing exclusively sp orbitals is viewed as great challenge in chemistry, physics, spintronics and materials science. Here we describe a series of room temperature organic magnets prepared by a simple and controllable route based on the substitution of fluorine atoms in fluorographene with hydroxyl groups. Depending on the chemical composition (an F/OH ratio) and sp3 coverage, these new graphene derivatives show room temperature antiferromagnetic ordering, which has never been observed for any sp-based materials. Such 2D magnets undergo a transition to a ferromagnetic state at low temperatures, showing an extraordinarily high magnetic moment. The developed theoretical model addresses the origin of the room temperature magnetism in terms of sp2-conjugated diradical motifs embedded in an sp3 matrix and superexchange interactions via -OH functionalization.