The next generation of cellular networks will be characterized by softwarized, open, and disaggregated architectures exposing analytics and control knobs to enable network intelligence via innovative data-driven algorithms. How to practically realize this vision, however, is largely an open problem. For a given network optimization/automation objective, it is currently unknown how to select which data-driven models should be deployed and where, which parameters to control, and how to feed them appropriate inputs. In this paper, we take a decisive step forward by presenting and prototyping OrchestRAN, a novel orchestration framework for next generation systems that embraces and builds upon the Open Radio Access Network (RAN) paradigm to provide a practical solution to these challenges. OrchestRAN has been designed to execute in the non-Real-time (RT) RAN Intelligent Controller (RIC) and allows Network Operators (NOs) to specify high-level control/inference objectives (i.e., adapt scheduling, and forecast capacity in near-RT, e.g., for a set of base stations in Downtown New York). OrchestRAN automatically computes the optimal set of data-driven algorithms and their execution location (e.g., in the cloud, or at the edge) to achieve intents specified by the NOs while meeting the desired timing requirements and avoiding conflicts between different data-driven algorithms controlling the same parameters set. We show that the intelligence orchestration problem in Open RAN is NP-hard, and design low-complexity solutions to support real-world applications. We prototype Orches-tRAN and test it at scale on Colosseum, the world's largest wireless network emulator with hardware in the loop. Our experimental results on a network with 7 base stations and 42 users demonstrate that OrchestRAN is able to instantiate data-driven services on demand with minimal control overhead and latency.