In England, though, doubts remain after his performances for Manchester United and Chelsea did not quite meet huge expectations, while among Argentine fans there are those who cannot forgive him for the country's dismal 2002 World Cup campaign.
The pluses, however, far outweigh the minuses, particularly after he led Estudiantes to a fourth South American Libertadores Cup title in 2009, three years after his return home.
Much more than just the captain of Estudiantes, Veron is the club's elder statesman, over and above directors twice his age, funding from the fortune he amassed in Europe facilities for the club in La Plata, the capital of Buenos Aires province.
Veron, shaven-headed with a goatee, has for some time shown an inclination towards becoming club president in the long term.
He hinted as much in a message he posted during the week on the club's website to the fans.
"When I look back [at the team's achievements since coming home] I realise it was worth it and I want to carry on planning for Estudiantes to carry on growing because there's still a lot to do and improve," Veron wrote.
"I can't imagine myself far from the club after my retirement," he added at a news conference.
"There are no regrets. I just would have liked to play a Champions League final... [and] win something with the national team," Veron, who reached the semi-finals of Europe's elite club competition with Manchester United 10 years ago, told reporters.
An immediate managerial position may not be too far away for Veron, however, with Argentina now coached by former Estudiantes player and trainer Alejandro Sabella.
Veron, a Serie A champion with Lazio in 2000 before his much heralded move to the English Premier League, recomposed his image with a majority of Argentine fans after he made a comeback for his country in the 2007 Copa America in Venezuela in a side also boasting Juan Roman Riquelme and Lionel Messi that lost to Brazil in the final.
A picture of where Veron stands vis-a-vis with the ills of the Argentine game, notably a major hooligan problem with the violent, so-called "barrabravas", was seen at an Estudiantes home game earlier this season.
Hooligans threw flares onto the pitch from behind the visiting goalkeeper's net, causing him to become disorientated and the referee to abandon the match after just 13 minutes.
Veron, followed soon after by other senior players, went behind the goal to remonstrate with the young fans who had clambered up the perimeter fence, shouting at them to "get down or I'll beat you up."
It is rare for players or coaches to stand up to the violent and influential hooligans, who control many of Argentine football's peripheral business such as parking and vending outside grounds, and hold directors to ransom for tickets and travel expenses to away matches.
Veron, a player who stood out for his busy, all-running style in central midfield, has earned the respect of his peers and enemies enough to suggest there might be important benefits for the Argentine game if he is allowed to ho
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