Communication overhead is one of the major obstacles to train large deep learning models at scale. Gradient sparsification is a promising technique to reduce the communication volume. However, it is very challenging to obtain real performance improvement because of (1) the difficulty of achieving an scalable and efficient sparse \textit{allreduce} algorithm and (2) the sparsification overhead. This paper proposes O$k$-Top$k$, a scheme for distributed training with sparse gradients. O$k$-Top$k$ integrates a novel sparse allreduce algorithm (less than 6$k$ communication volume which is asymptotically optimal) with the decentralized parallel Stochastic Gradient Descent (SGD) optimizer, and its convergence is proved. To reduce the sparsification overhead, O$k$-Top$k$ efficiently selects the top-$k$ gradient values according to an estimated threshold. Evaluations are conducted on the Piz Daint supercomputer with neural network models from different deep learning domains. Empirical results show that O$k$-Top$k$ achieves similar model accuracy to dense allreduce. Compared with the optimized dense and the state-of-the-art sparse allreduces, O$k$-Top$k$ is more scalable and significantly improves training throughput (e.g., 3.29x-12.95x improvement for BERT on 256 GPUs).