Veron, who is the club's technical secretary and was sporting director last season, signed a new player's contract until next June on Thursday and will play for them in the 2013-14 Argentine first division league season.
"I don't think I'm in the form of that time (in 2009) when we won the Copa Libertadores, but I'm just as motivated because I love playing football," the 38-year-old playmaker told Radio Del Plata earlier this week.
Veron kept fit playing for a team that won the La Plata amateur league, while Estudiantes finished 14th in the 'Final' championship, second of two in the season, last month.
He started his career at Estudiantes, his hometown club, before moving to Argentine giants Boca Juniors in 1996.
After making his international debut, Veron was quickly scouted by Italian side Sampdoria, where he played under Sven-Goran Eriksson for two years before joining Parma for £15 million.
Eriksson had moved to Lazio, and the Swede bought Veron for a second time, with the pair famously winning the Italian Serie A and Coppa double in 2000.
United soon swooped, shelling out £28m on Veron, but his time at Old Trafford was not a huge success, with the deep-lying playmaker struggling to adapt to the different pace and tactics of English football.
Sir Alex Ferguson famously called journalists "all f***ing idiots" when they questioned Veron's ability, but he was eventually sold to Chelsea for a cut-price £15m.
He only played seven Premier League games for the Blues before returning to Italy with Inter, where he spent three years before deciding to go back to his alma mater.