Albion paid a hefty fee to Boca Juniors last month - believed to be around £600,000 - to cut his season-long loan deal short with the Supaliga title-chasers.
Mac Allister has just completed a successful Olympic qualifying campaign with Argentina under-23s and is now available for Albion's final 12 matches of the Premier League season, starting at Bramall Lane on February 22.
Albion, who hover just three points above the relegation zone, signed the midfielder on a four-year contract in January 2019 for a fee of around £7m. Mac Allister was then unable to play due to work permit issues and was loaned back to Argentinos Juniors.
He soon switched to cross-city rivals Boca and impressed to such an extent that he was called-up to Argentina national squad and made his full debut against Chile at the Los Angeles Memorial Coliseum on 5 September.
He is one of South America's brightest young talents and tipped by some to one day succeed Lionel Messi as Argentina's next No 10.
His displays at the Olympic qualifiers added weight to that argument, where he scored twice and provided one assist as Argentina finished top of the qualifying group despite losing Sunday’s final game 3-0 to Brazil, who also qualified.
The 21-year-old of Scottish heritage is slight of build, not the fastest but has an excellent range of passing and constantly looks to sneak away from defenders and arrive in the box. The prospect of him linking with Brighton's other young and creative midfielders, Steven Alzate and Leandro Trossard, is quite a tantalising one.
So far this season Mac Allister has dazzled in Buenos Aires at the La Bombonera and lit up the his country's Olympic qualifying campaign against South America's finest young talents - but the one question remains: Can he do it on a cold Saturday afternoon against Chris Wilder's Sheffield United at Bramall Lane?
"He’ll be joining up with the rest of the lads before Sheffield United," said Brighton head coach Graham Potter. "We are looking forward to working with him and meeting him.
“He’s a midfield player that can play off the side, mainly as a No 10.
“Again, it’s important we get him here and work with him, as well as helping him settle into another country - then we will see where we go from there."