Despite global conservation efforts, biodiversity continues to decline, causing many species to face extinction. These efforts include designing protected areas to function as ecologically connected networks for habitat and movement pathway conservation. Ecological connectivity is defined as the connectivity of landscapes and seascapes that allows species to move and ecological processes to function unimpeded. It facilitates long-term species persistence and resilience, mitigates the impact of habitat fragmentation due to climate change and land-use change, and addresses ecological processes that support ecosystems. Thus, ecological connectivity is key in the design of habitat conservation networks. To incorporate many complicating factors in this process, it relies on decision-support frameworks to decide which areas to include to protect biodiversity while minimizing cost. Various approaches emerged to deal with the computational complexity involved in habitat conservation design. However, despite the importance of designing ecologically connected conservation networks, these widely used decision-support frameworks do not offer functionality to optimize ecological connectivity directly during conservation design. Here, we present a fast, exact method to use connectivity metrics during the biodiversity conservation design process. Our method is exact in the sense that it always returns optimal solutions in our model. We extend an existing Reserve Selection problem (RSP) formulation with vertex-weighted connectivity constraints to include edge-weighted connectivity constraints. Further, we describe two novel variations of the RSP to directly optimize over connectivity metrics, one with cost minimization and one with a fixed cost. We introduce Coco, an open-source decision-support system to design ecologically connected conservations. Coco provides an integer linear programming (ILP) method to include connectivity in conservation design. To this end, we formulate our novel RSP variations as an ILP. We test Coco on simulated data and two real datasets, one dataset of the Great Barrier Reef and a large-scale dataset of the marine area in British Columbia. We compare the performance of Coco to Marxan Connect and show that Coco outperforms Marxan Connect both in runtime and solution quality. Further, we compare the results of our proposed methods to the existing RSP formulation and show that our novel methods significantly increase connectivity at a lower cost.