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The trend towards denser base station deployment and multi-band operations in emerging cellular networks has made mobility management and handover (HO) optimization a formidable challenge. The challenge is further aggravated by the scarcity of practical multi-objective mobility management solutions optimizing both intra and inter frequency HO. This paper presents a holistic multi-objective mobility management solution for both intra and inter frequency HO employing multiple parameters of standardized HO events A2, A3, and A5. We formulate a multi-objective optimization problem to determine the optimal parameter settings that jointly optimize four key performance indicators: number of HO failures, HO latency, signaling overhead and number of radio link failures. We leverage soft actor-critic reinforcement learning (RL) to solve the multi-objective problem. To mitigate the risk of performance deterioration resulting from direct interactions between live network and RL-agent during training, this paper proposes a mobility management framework that develops and employs a digital twin (DT) as the training environment. To develop a cellular network DT for mobility management and HO optimization, we present a tri-pronged approach including realistic network deployment, realistic user mobility and 3GPP HO events. Results show that the proposed DT-trained RL solution for the multiobjective optimization can converge 7x faster than the brute force method with negligible loss in the value of the objective function. An analysis of the individual KPI values reveal a strong trade-off between HO signaling overhead and radio link failures. I …