Ferromagnets in contact with a topological insulator have become appealing candidates for spintronics due to the presence of Dirac surface states with spin-momentum locking. Because of this, bilayer Bi2Se3-EuS structures, for instance, show a finite magnetization at the interface at temperatures well exceeding the Curie temperature of bulk EuS. Here, we determine theoretically the effective magnetic interactions at a topological insulator-ferromagnet interface above themagnetic ordering temperature. We show that by integrating out the Dirac fermion fluctuations an effective Dzyaloshinskii-Moriya interaction and magnetic charging interaction emerge. As a result, individual magnetic skyrmions and extended skyrmion lattices can form at the interfaces of ferromagnets and topological insulators, the first indications of which have been very recently observed experimentally.