This study investigates the validity of Wagner’s law and Keynesian hypothesis of the longrun relationship between government expenditure and economic growth in Tanzania using annual time series data from 1978 to 2014. The data series were tested for stationarity using Phillips-Perron unit root test and the results revealed that they were all stationary and integrated of order one I(1). The Johansen test of cointegration revealed that there are cointegrating vectors in the system which indicates the existence of long-run equilibrium relationship among the variables. The Granger causality test was performed within vector error correction model and the results revealed strong support for both Wagner’s law and Keynesian hypothesis when government expenditure was taken at its aggregate level. At the disaggregated levels, the results depict that recurrent expenditure and development expenditure from foreign sources promote economic growth hence supporting the Keynesian hypothesis. Wagner’s law was only supported in one instance where causality runs from economic growth to development expenditure from domestic sources. These results highlight the need for policy makers to direct development expenditure from domestic sources to sectors that stimulate economic growth.