It can be done immediately - and takes 30 seconds.
Tell the school that issues your visa that you wish to transfer.
They DO NOT have the right to terminate your visa if you tell them you want to transfer to a competitor (if they threaten to do so then YOU must call the SEVIS helpline [google!!] and tell "Immigration" what the school said or did).
The visa issuing people at the school you wish to leave need only to enter your file on the SEVIS website and click on "transfer out".
The school you want to go to should click on their records and click "transfer in".
Job done.