The provision of Storage as a Service (STaaS) in many geo-distributed datacenters by several Cloud Storage Providers (CSPs) has made online cloud storage a great choice for replicating and distributing objects that are accessed worldwide. Online Social Networks (OSN) such as Facebook and Twitter have billions of active users worldwide accessing shared objects. These users expect to access these objects within a tolerable time. To minimize users’ access latency time of these objects, OSN service providers must host several replicas of objects in many datacenters. However, this replication process produces a higher monetary cost. This paper addresses crucial issues, including how many replicas are required to fulfil the expected workload of the object and the optimal datacenters to host these replicas to reduce latency time for users and monetary costs for OSN service providers. Two online algorithms are proposed to determine the suitable number of replicas for each object and the optimal placement of these replicas. The DTS algorithm establishes the replication and placement of objects using deterministic time slots, while the RTS algorithm is based on randomized time slots. Experimental results show the effectiveness of the proposed algorithms for producing latency time below certain thresholds and reducing the monetary cost.