Data Migration or Sharded Cluster to new Cluster
Migrating an existing sharded cluster to new hardware

If you want to migrate a sharded cluster to new hardware, there is a tutorial in the MongoDB manual: Migrate a Sharded Cluster to Different Hardware

Migrating data in an existing sharded cluster to a new cluster

There is no officially supported process to migrate documents between two different MongoDB clusters (at least as at MongoDB 2.6), but you do have a few options:


A typical approach is via backup &amp; restore of the sharded cluster, but that involves some down time or a custom script to sync up changes that occurred while you were loading data into the new cluster.
The team at Mailbox has open sourced a set of Python scripts called Hydra which specifically aim to enable live migration of sharded  collections. For more background details see: Scaling MongoDB at Mailbox.


I haven't personally tried Hydra (and there is currently a caveat in the Github repo that the authors only tested with MongoDB 2.2.3 on Ubuntu 12.04), however it seems like a promising approach.