Segmentation of blood cells is a prerequisite step in automated morphological analysis of blood smear images, cell count determination and diagnosis of various diseases such as leukemia. It is extremely challenging due to different sizes, shapes, morphological characteristics and overlapping of blood cells. Due to its complicated nature, it is generally performed as a sequence of steps. However, sequential segmentation results in restricted accuracy due to cascading of errors that creep during each stage. On the contrary, pixel-wise segmentation of blood cells is a single step task and gives promising results. In this paper, we propose LeukoSegmenter, a double encoder-decoder for precise pixel-wise segmentation of leukocytes from blood smear images. It uses pre-trained ResNet18 based encoders and U-Net based decoders. Feature maps obtained from the first network are utilised as attention maps. These are used as input in conjunction with the original 3-channel image to obtain final mask from the second network. This mechanism allows the latter encoder-decoder pair to focus explicitly on leukocytes and ignore other blood cells and debris, thus improving the segmentation accuracy. Experiments on ALL-IDB1 dataset show that the proposed LeukoSegmenter achieves intersection-over-union score of 94.6827% and Dice score of 97.1987% which is superior than that of state-of-the-art methods.