Using data from the three Swarm satellites, we study the ionospheric response to the intense geomagnetic storm of June 22-23, 2015. With the minimum SYM-H excursion of −207 nT, this storm is so far the second strongest geomagnetic storm in the current 24th solar cycle. A specific configuration of the Swarm satellites allowed investigation of the evolution of the storm-time ionospheric alterations on the day-and the nightside quasi-simultaneously. With the development of the main phase of the storm, a significant dayside increase of the vertical total electron content (VTEC) and electron density Ne was first observed at low latitudes on the dayside. From ~22 UT of 22 June to ~1 UT of 23 June, the dayside experienced a strong negative ionospheric storm, while on the nightside an extreme enhancement of the topside VTEC occurred at mid-latitudes of the northern hemisphere. Our analysis of the equatorial electrojet variations obtained from the magnetic Swarm data indicates that the storm-time penetration electric fields were, most likely, the main driver of the observed ionospheric effects at the initial phase of the storm and at the beginning of the main phase. The dayside ionosphere first responded to the occurrence of the strong eastward equatorial electric fields. Further, penetration of westward electric fields led to gradual but strong decrease of the plasma density on the dayside in the topside ionosphere. At this stage, the disturbance dynamo could have contributed as well. On the nightside, the observed extreme enhancement of the Ne and VTEC in the northern hemisphere (i.e., the summer hemisphere) in the topside ionosphere was most likely due to the combination of the prompt penetration electric fields, disturbance dynamo and the storm-time thermospheric circulation. From ~2.8 UT, the ionospheric measurements from the three Swarm satellites detected the beginning of the second positive storm on the dayside, which was not clearly associated with electrojet variations. We find that this second storm might be provoked by other drivers, such as an increase in the thermospheric composition.