Mattock, 20, who can also play in midfield, will stay at Bramall Lane until the end of the season. He will go straight into Micky Adams' squad for Saturday's clash at Coventry.
Adams told the club's official website: "Joe's young and enthusiastic and certainly gives us competition for places.
"He had an injury at the start of the season which limited his opportunities for West Brom but he's naturally left-footed and having him here will help us climb the table."
Mattock made his debut for hometown club Leicester as a 16-year-old in 2007 and went on to make more than 50 appearances for the Foxes before joining West Brom for an undisclosed fee in August 2009.