The 27-year-old, who has put pen to paper on a two-and-a-half-year contract with the Sky Bet League 1 club, made only three appearances for Albion but has picked up plenty of experience during a number of loan spells.
Manager Mark Robins told Scunthorpe's official website: "Luke is a player who has been on our radar for a while, and has certainly been on the top of our list.
"I'm really pleased to get a goalkeeper of Luke's quality and look forward to working with him over the next two-and-a-half years.
"He's been at a Premier League club for a very long time and possesses all the attributes you require from a goalkeeper."
Daniels said: "I'm delighted to be here and can't wait to get started.
"I've been around the club and it's definitely one that's looking to get to the Championship quickly, so that matches my goals as well."
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