(1) Background: Bioreactors mimic the natural environment of cells and tissues by providing a controlled micro-environment. However, their design is often expensive and complex. Herein, we have introduced the development of a low-cost compression bioreactor which enables the application of different mechanical stimulation regimes to in vitro tissue models and provides the information of applied stress and strain in real-time. (2) Methods: The compression bioreactor is designed using a mini-computer called Raspberry Pi, which is programmed to apply compressive deformation at various strains and frequencies, as well as to measure the force applied to the tissue constructs. Besides this, we have developed a mobile application connected to the bioreactor software to monitor, command, and control experiments via mobile devices. (3) Results: Cell viability results indicate that the newly designed compression bioreactor supports cell cultivation in a sterile environment without any contamination. The developed bioreactor software plots the experimental data of dynamic mechanical loading in a long-term manner, as well as stores them for further data processing. Following in vitro uniaxial compression conditioning of 3D in vitro cartilage models, chondrocyte cell migration was altered positively compared to static cultures. (4) Conclusion: The developed compression bioreactor can support the in vitro tissue model cultivation and monitor the experimental information with a low-cost controlling system and via mobile application. The highly customizable mold inside the cultivation chamber is a significant approach to solve the limited customization capability of the traditional bioreactors. Most importantly, the compression bioreactor prevents operator- and system-dependent variability between experiments by enabling a dynamic culture in a large volume for multiple numbers of in vitro tissue constructs.