Provided are a computer program product, system, and method for establishing copy pairs from primary volumes to secondary volumes in multiple secondary storage systems for a failover session. For each of the copy pairs, data is mirrored from the primary storage system to the associated secondary storage system in the copy pair. A failure is detected at the primary storage system. Selection is made of a selected secondary storage system of the secondary storage systems in response to detecting the failure, wherein a plurality of the secondary storage systems are available for selection. The selected secondary storage system is indicated as a new primary storage system to which host requests are directed.