Tile-based many-core architectures are extensively used in modern system-on-chip designs to achieve scalable computing performance with adequate energy efficiency. Heterogeneity is the key element to boost computing performance and keep energy consumption under certain limits for several application domains. However, the steady increase of using many custom heterogeneous tiles leads to an expansion in design and integration cost with limited tiles re-usability. The recent widespread of open-source RISC-V ISA provides the potential to develop modular compute units that can be used for many application domains with high reduction in non-recurring engineering costs. The motivation of this work is to bring design modularity and adaptability features for heterogeneous tile-based many-core architectures by increasing their flexibility to realize different many-core configurations with less design time and costs. In this work, AGILER is proposed as an adaptive tile-base many-core architecture for heterogeneous RISC-V based processors. The proposed architecture consists of modular and adaptable heterogeneous multi-/single-core compute tiles that supports 32-/64-bit RISC-V ISAs with different memory hierarchies. Inter-tile communication is developed based on a scalable network-on-chip architecture to achieve a high degree of system scalability. AGILER supports run-time adaptation through a custom internal reconfiguration manager for dynamic and partial reconfiguration over Xilinx FPGAs. Evaluation results demonstrate that the proposed architecture features a scalable computing performance up to 685 MOPS for 8\times 32 -bit tiles and 316 MOPS for 8\times 64 -bit tiles with a scalable memory bandwidth up to 7.4 GB/s. AGILER is evaluated on Xilinx Virtex Ultrascale+ FPGA with a maximum reconfiguration time of 38.1 ms for a single compute tile.