Starting from the London-type model, we study the domain structures in ferromagnetic superconductors taking account of the nucleation of vortices and antivortices coupled to the magnetic texture. We predict that the coupling between domains and vortices results in the formation of two energetically favorable domain configurations: (i) a Meissner-type vortex-free configuration with strong domain shrinking and (ii) a more rare domain configuration with a dense vortex-antivortex lattice. The switching between these configurations is shown to result in the first-order phase transitions which could be observable in superconducting uranium-based compounds.