It will depend on the exchange since each exchange can set their own rules regarding withdrawals.
However, assuming transaction is sent immediately when you place it on the exchange:
The transaction should show up on the block chain in about 2 minutes (monero block time)
It will appear as part of your balance, but not your unlocked balance until the transaction is 10 confirmations deep I believe.
So given those stipulations, the quickest you'd be able to move your monero from the web wallet would be 20 minutes from when you sent the monero from the exchange.
As a general real world answer, I'd say you should be able to spend your funds about 30 minutes after making a transaction.