As concerto49 said, it won't be cheap. I have something like this in place, shipping disks/tapes back and forth quarterly for a remote disaster recovery backup procedure, and I am still looking for a cheaper solution.
Backblaze does something like that (they can ship a USB drive with your data), but price is still somewhat high ($189 per drive, on top of the standard subscription) and data need to be transferred to Backblaze servers (something I don't want to do).
Amazon AWS Import/Export service is cheaper ($80 per drive plus shipping fees), but I rather avoid Amazon AWS services.
I had high hopes about low-cost Raspberry Pi colocation services, because a Raspberry plus Usb drive or high capacity stick will be cheap to ship and handle, but they never materialized. As proof of concept, I have some Rapsberry Pi's in a server rack for quite some time now; I had many doubt about stability of this consumer-grade hardware, but they work flawlessly (with a high quality power supply).