Clough told the club's official website: "We're delighted to have been able to land a goalkeeper of David's quality at such short notice.
"I would like to thank Liverpool for allowing David to join us; it has been a frantic few hours since Wednesday evening but we are pleased to have a solution now."
Meanwhile, defender Miles Addison is set to undergo an operation on his troublesome foot injury in America next week.
Clough added: "He's 21 and has got another 10 years or so in him, but if we don't fix it now, he will always be dogged by the problem. We've found somebody in San Francisco who specialises in this kind of injury, so we're flying him over there next week."