The expansion of agricultural frontiers in Brazil has caused substantial changes in land use and land cover. This research aims to analyze the space-time dynamics of soybeans and cattle production in the Brazilian territory during the period 1991–2015. The spatial analysis adopted the following procedures: (a) The change vector from the annual calculation of the midpoint of production; (b) mapping of the growth and acceleration rates of the two productions, and (c) mapping of the correlation between the time series of soybean and cattle. The results showed high rates of growth and acceleration for soy production in the South, Central-West and Matopiba regions. The growth acceleration rate identified the long-term deviations that characterized the effective soybean and cattle expansion areas. The results demonstrated the effects of Brazil’s soy moratorium contained soybean expansion into the Amazon region. However, as a side effect, the soybean production replaced cattle production in the savanna region, which in turn, migrated to the Amazon rainforest. Therefore, the present study highlights the importance of public policies that comprehensively understand the spatial-temporal dynamics of Brazilian agriculture to promote sustainable land-use practices.