When bitcoin-qt is first run, it should automatically create a .bitcoin directory in the users "home" directory aka ~/.bitcoin and it should prompt to ask where to set the datadir to. If you've already used that, you can try a couple of things to "move" the datadir:
In the .bitcoin directory, if you create a "bitcoin.conf" file... you can add the
datadir option and set that to where you want the blocks stored...
datadir=full/path/to/your/bitcoin/datadir
Alternatively, simply start bitcoin-qt using the "-choosedatadir" option... it'll prompt you again to choose where you want the datadir to be set to.
bitcoin-qt -choosedatadir
NOTE: be wary of the "discard blocks after verification" (prune) option... that could cause problems later if you need to import private keys or rescan/reindex. I would suggest leaving it "UNCHECKED" if you have the storage space to store the full blockchain (350+gigs)
Also note that neither of these options will "move" the current contents of the datadir to the new location... so bitcoin core will start syncing from block 0 again.