Machine learning has been employed for various mapping and modeling tasks using input variables from different sources of remote sensing data. For feature selection involving high- spatial and spectral dimensionality data, various methods have been developed and incorporated into the machine learning framework to ensure an efficient and optimal computational process. This research aims to assess the accuracy of various feature selection and machine learning methods for estimating forest height using AISA (airborne imaging spectrometer for applications) hyperspectral bands (479 bands) and airborne light detection and ranging (lidar) height metrics (36 metrics), alone and combined. Feature selection and dimensionality reduction using Boruta (BO), principal component analysis (PCA), simulated annealing (SA), and genetic algorithm (GA) in combination with machine learning algorithms such as multivariate adaptive regression spline (MARS), extra trees (ET), support vector regression (SVR) with radial basis function, and extreme gradient boosting (XGB) with trees (XGbtree and XGBdart) and linear (XGBlin) classifiers were evaluated. The results demonstrated that the combinations of BO-XGBdart and BO-SVR delivered the best model performance for estimating tropical forest height by combining lidar and hyperspectral data, with R2 = 0.53 and RMSE = 1.7 m (18.4% of nRMSE and 0.046 m of bias) for BO-XGBdart and R2 = 0.51 and RMSE = 1.8 m (15.8% of nRMSE and −0.244 m of bias) for BO-SVR. Our study also demonstrated the effectiveness of BO for variables selection; it could reduce 95% of the data to select the 29 most important variables from the initial 516 variables from lidar metrics and hyperspectral data.