In the era of the Paris Agreement and global efforts to reduce carbon emissions, an increasing share of investments needs to be aligned with net-zero targets in order to finance the transition to a low-carbon economy. We formulate two stochastic optimal control problems that allow investors to align their portfolios with net-zero objectives. Both problems seek to maximize the expected logarithmic portfolio return while either (I) minimizing the time-weighted carbon footprint of the portfolio or (II) minimizing the time-weighted squared relative deviation from a prescribed net-zero target path. For both problems, we derive closed-form optimal investment strategies. In the first case, the optimal strategy is obtained from the unconstrained benchmark strategy through a simple adjustment of the asset return drifts, whereas the second problem requires adjustments to both the drift vector and the covariance matrix. Using real-world data, we show that the proposed strategies substantially reduce portfolio carbon emissions while delivering financial performance comparable to that of the corresponding unadjusted benchmark strategy.