Westlake will stay with Mansfield until January 5 and go straight into manager Paul Cox's squad for Saturday's home game against Morecambe.
The 22-year-old has made 10 appearances for the Blades this season, but recently-appointed United boss Nigel Clough feels Westlake will benefit from the chance to play regular first-team football.
Westlake began his career with Walsall and featured on 67 occasions for the Saddlers, before penning a two-year deal at Bramall Lane in June 2012.
He made his Football League debut as an 18-year-old in August 2009, and featured on 76 occasions during his time at the Banks Stadium.
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