Corryvreckan is a versatile, highly configurable software with a modular structure designed to reconstruct and analyse test beam and laboratory data. It caters to the needs of the test beam community by providing a flexible offline event building facility to combine detectors with different readout schemes, with or without trigger information, and includes the possibility to correlate data from multiple devices based on timestamps. Hit timing information, available with high precision from an increasing number of detectors, can be used in clustering and tracking to reduce combinatorics. Several algorithms, including an implementation of Millepede-II, are provided for offline alignment. A graphical user interface enables direct monitoring of the reconstruction progress and can be employed for quasi-online monitoring during data taking. This work introduces the Corryvreckan framework architecture and user interface, and provides a detailed overview of the event building algorithm. The reconstruction and analysis capabilities are demonstrated with data recorded at the DESY II Test Beam Facility using the EUDAQ2 data acquisition framework with an EUDET-type beam telescope, a Timepix3 timing reference, a fine-pitch planar silicon sensor with CLICpix2 readout and the AIDA Trigger Logic Unit. The individual steps of the reconstruction chain are presented in detail.