Provided are a computer program product, system, and method for releasing space allocated to a space efficient target storage in a copy relationship with a source storage. Source and target copy relationships indicate source data in the source storage to copy to target data in the target storage. The source copy relationship indicates source data that need to be copied to the target data before being updated, and the target copy relationship indicates target data tracks updated with data copied from corresponding source data. An operation is initiated that results in terminating the source and target copy relationships. Space allocated to the target data for the source and target copy relationships is released in response to determining that the target storage comprises the space efficient storage. The source and target copy relationships are removed.