Provided are a computer program product, system, and method for migrating jobs from a source server from which data is migrated to a target server to which the data is migrated. Mirrored data is copied from a source storage to a target storage. A determination is made of at least one eligible job of the jobs executing in the source server having execution characteristics indicating that the job is eligible for migration to the target server. The determined at least one eligible job is migrated to the target server to execute on the target server and perform operations with respect to the mirrored data in the target storage. The migrated eligible job is disabled at the source server.