Gamification has been applied in software engineering to improve quality and results by increasing people's motivation and engagement. A systematic mapping has identified research gaps in the field, one of them being the difficulty of creating an integrated gamified environment comprising all the tools of an organization, since most existing gamified tools are custom developments or prototypes. In this paper, we propose a gamification software architecture that allows us to transform the work environment of a software organization into an integrated gamified environment, i.e., the organization can maintain its tools, and the rewards obtained by the users for their actions in different tools will mount up. We developed a gamification engine based on our proposal, and we carried out a case study in which we applied it in a real software development company. The case study shows that the gamification engine has allowed the company to create a gamified workplace by integrating custom developed tools and off-the-shelf tools such as Redmine, TestLink, or JUnit, with the gamification engine. Two main advantages can be highlighted: (i) our solution allows the organization to maintain its current tools, and (ii) the rewards for actions in any tool accumulate in a centralized gamified environment.