The user-centric cooperative transmission provides a compelling way to alleviate frequent handovers caused by an ever-increasing number of randomly deployed base stations (BSs) in ultra-dense networks (UDNs). This paper proposes a new user-centric cooperative transmissions-based handover scheme, i.e., the group-cell handover (GCHO) scheme, with the aim of reducing the handover rate in UDNs. In the proposed scheme, the boundary of the cooperating cluster depends on the distance among the user equipment (UE) and cooperating BSs. The new scheme captures the dynamicity and irregularity of the cooperating cluster topology resulting from randomly distributed BSs. Based on stochastic-geometry tools where BSs locations are modeled as the Poison point process (PPP), we derive an analytical expression of the handover rate for the UE with an arbitrary movement trajectory. Furthermore, a GCHO skipping (GCHO-S) scheme is proposed to minimize the handover cost, i.e., the percentage of time wasted in handover signaling in user-centric cooperative transmissions scenarios. The numerical results show that the GCHO scheme decreases the handover rate by 42.3% and 72.7% compared with the traditional single BS association and fixed-region cooperative network topology handover approaches, respectively. Moreover, under the same group-cell size and constant velocity, the GCHO-S scheme diminishes the handover cost by 50% against the GCHO scheme.