In this paper, we propose an effective knowledge transfer framework to boost the weakly supervised object detection accuracy with the help of an external fully-annotated source dataset, whose categories may not overlap with the target domain. This setting is of great practical value due to the existence of many off-the-shelf detection datasets. To more effectively utilize the source dataset, we propose to iteratively transfer the knowledge from the source domain by a one-class universal detector and learn the target-domain detector. The box-level pseudo ground truths mined by the target-domain detector in each iteration effectively improve the one-class universal detector. Therefore, the knowledge in the source dataset is more thoroughly exploited and leveraged. Extensive experiments are conducted with Pascal VOC 2007 as the target weakly-annotated dataset and COCO/ImageNet as the source fully-annotated dataset. With the proposed solution, we achieved an mAP of 59.7 % detection performance on the VOC test set and an mAP of 60.2 % after retraining a fully supervised Faster RCNN with the mined pseudo ground truths. This is significantly better than any previously known results in related literature and sets a new state-of-the-art of weakly supervised object detection under the knowledge transfer setting. Code: https://github.com/mikuhatsune/wsod_transfer.