The Aston Villa starlet will join the Blades on a permanent deal with Villa holding a buyback option, 24 hours after a similar move for Aaron Ramsey, who joined Burnley.
Sheffield United lost their main man up front Iliman Ndiaye earlier in the window to Marseille, and are now close to landing his replacement.
The Villans have sanctioned the move as they look to balance their books, but the club have not ruled out replacing the young forward before the transfer window closes.
The 21-year-old is regarded as one of England's best young attackers having played a starring role in England under-21s success at the European Championships this summer.
After rising through the ranks at Bodymoor Heath, Archer enjoyed a loan spell with Solihull Moors in 2020/21 where he scored four goals in 21 appearances.
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It was the following year when he joined Preston that he started his rise to prominence, scoring seven goals in 20 Championship appearances.
Last term he joined Middlesbrough on loan in January and almost guided them to promotion, scoring 11 goals and grabbing six assists in just 23 appearances to take them into the play-offs where they fell short.
Premier League football is the natural next step and with regular football not guaranteed under Unai Emery, he'll be hoping to make an impression at Bramall Lane.