The emerging and vast adoption of the Internet of Things (IoT) has sprung a plethora of research works regarding the potential benefits in smart agriculture. A popular implementation involves the deployment of Wireless Sensor Networks (WSNs), which embed low energy consumption sensory nodes to capture the critical environmental parameters prevailing on the farms. However, to manage the ever-increasing volumes of raw data successfully, new approaches must be explored. Under this scope, current work reports on the design and development of an IoT system, having in mind the case of olive groves, which are considered the dominant sector for agricultural activity in the Mediterranean Basin. The system incorporates the cloud/fog computing paradigm to equip the olive growers with a low-cost solution for accurate, reliable, and almost real-time monitoring of their crops. Its core is based on a three-layered network architecture, capable of dynamically balancing the generated load, by pushing cloud-elastic resources to the underlying fog network. As such, the premise of the approach lies in the conforming character of the system that allows for targeted alterations to its operational functionality to meet stringent latency and traffic load environmental monitoring constraints. To evaluate the performance of the proposed architecture, a demo prototype is developed and deployed in the facilities of the Ionian University. Experimental results illustrate the efficiency, flexibility, and scalability of the approach in terms of latency, achieving response time reduction across all platforms, a subject of the utmost importance when it comes to precision agriculture of the future. Moreover, it is shown that the system is capable of dynamic functionality adaptation, to meet network traffic load constraints, achieving high throughput (on average 95%) and addressing potential environmental dangers to olive oil production.