We propose Shard Scheduler, a system for object placement and migration in account-based sharded blockchains. Our system calculates optimal placement and decides on object migrations across shards. It supports complex multi-account transactions caused by smart contracts. Placement and migration decisions made by Shard Scheduler are fully deterministic, verifiable, and can be made part of the consensus protocol. Shard Scheduler reduces the number of costly cross-shard transactions, ensures balanced load distribution and maximizes the number of processed transactions for the blockchain as a whole. To this end, it leverages a novel incentive model motivating miners to maximize the global throughput of the entire blockchain rather than the throughput of a specific shard. In our simulations, Shard Scheduler can reduce the number of costly cross-shard transactions by half while ensuring equal load and increasing throughput more than 2 fold when using 60 shards. We also implement and evaluate Shard Scheduler on Chainspace, more than doubling its throughput and reducing user-perceived latency by 70% when using 10 shards.