Virtual data integration is the current approach to go for data wrangling in data-driven decision-making. In this paper, we focus on automating schema integration, which extracts a homogenised representation of the data source schemata and integrates them into a global schema to enable virtual data integration. Schema integration requires a set of well-known constructs: the data source schemata and wrappers, a global integrated schema and the mappings between them. Based on them, virtual data integration systems enable fast and on-demand data exploration via query rewriting. Unfortunately, the generation of such constructs is currently performed in a largely manual manner, hindering its feasibility in real scenarios. This becomes aggravated when dealing with heterogeneous and evolving data sources. To overcome these issues, we propose a fully-fledged semi-automatic and incremental approach grounded on knowledge graphs to generate the required schema integration constructs in four main steps: bootstrapping, schema matching, schema integration, and generation of system-specific constructs. We also present NextiaDI, a tool implementing our approach. Finally, a comprehensive evaluation is presented to scrutinize our approach.