With the widespread popularity of cloud storage, a growing quantity of tenants prefer to upload their massive data to remote cloud data center for saving local cost. Due to the great market prospect, a large quantity of enterprises provide cloud storage services, which are equipped with different prices, reliability, security, and so on. Hence, outsourced data transfer has become a fundamental requirement for tenants to flexibly change cloud service providers (CSPs) to enjoy more suitable services. Nevertheless, how to guarantee the data integrity when the data are transferred from a cloud data center to another is a concern of tenants. To solve this concern, we design a new validation data structure, namely, counting Bloom filter tree (CBFT), which can be viewed as a specific binary tree based on CBF. Then, we present an efficient outsourced data transfer scheme supporting provable data deletion, in which tenants can flexibly change CSPs and transfer their outsourced data blocks from a cloud data center to another without retrieving them. At the same time, after the data are successfully transferred, tenants can validate the transferred data integrity and usability on the new cloud data center and permanently delete the transferred data from the old cloud data center. Moreover, the formal security analysis proves that our new solution can achieve all of the anticipant security goals without interaction with a third party. At last, we develop a prototype system and implement our new solution, thus providing accurate performance evaluation, which intuitively presents the high efficiency and practicality of our new solution.