Reversible data hiding (RDH) is an active area of research in the field of information security. In RDH, a secret can be embedded inside a cover medium. Unlike other data-hiding schemes, RDH becomes important in applications that demand recovery of the cover without any deformation, along with recovery of the hidden secret. In this paper, a new RDH scheme is proposed for performing reversible data hiding in encrypted images using a Fibonacci transform with an ensemble learning method. In the proposed scheme, the data hider encrypts the original image and performs further data hiding. During data hiding, the encrypted image is partitioned into non-overlapping blocks, with each block considered one-by-one. The selected block undergoes a series of Fibonacci transforms during data hiding. The number of Fibonacci transforms required on a selected block is determined by the integer value that the data hider wants to embed. On the receiver side, message extraction and image restoration are performed with the help of the ensemble learning method. The receiver will try to perform all possible Fibonacci transforms and decrypt the blocks. The recovered block is identified with the help of trained machine-learning models. The novelty of the scheme lies in (1) retaining the encrypted pixel intensities unaltered while hiding the data. Almost every RDH scheme described in the literature alters the encrypted pixel intensities to embed the data, which represents a security concern for the encryption algorithm; (2) Introducing an efficient means of recovery through an ensemble model framework. The majority of votes from the different trained models guarantee the correct recovery of the cover image. The proposed scheme enables reduction in the bit error rate during message extraction and contributes to ensuring the suitability of the scheme in areas such as medical image transmission and cloud computing. The results obtained from experiments undertaken show that the proposed RDH scheme was able to attain an improved payload capacity of 0.0625 bits per pixel, outperforming many related RDH schemes with complete reversibility.