Growth of the older adult population has led to an increasing interest in technology-supported aged care. However, the area has some challenges such as a lack of caregivers and limitations in understanding the emotional, social, physical, and mental well-being needs of seniors. Furthermore, there is a gap in the understanding between developers and ageing people of their requirements. Digital health can be important in supporting older adults wellbeing, emotional requirements, and social needs. Requirements Engineering (RE) is a major software engineering field, which can help to identify, elicit and prioritize the requirements of stakeholders and ensure that the systems meet standards for performance, reliability, and usability. We carried out a systematic review of the literature on RE for older adult digital health software. This was necessary to show the representatives of the current stage of understanding the needs of older adults in aged care digital health. Using established guidelines outlined by the Kitchenham method, the PRISMA and the PICO guideline, we developed a protocol, followed by the systematic exploration of eight databases. This resulted in 69 primary studies of high relevance, which were subsequently subjected to data extraction, synthesis, and reporting. We highlight key RE processes in digital health software for ageing people. It explored the utilization of technology for older user well-being and care, and the evaluations of such solutions. The review also identified key limitations found in existing primary studies that inspire future research opportunities. The results indicate that requirement gathering and understanding have a significant variation between different studies. The differences are in the quality, depth, and techniques adopted for requirement gathering and these differences are largely due to uneven adoption of RE methods.