Beckham's announcement that he is to retire at the end of the season has given way to raft of eulogies from former team-mates, managers and opponents, and one-time nemesis Simeone joined in lauding the 38-year-old's high-profile career.
"He has been a great professional, an extraordinary player and I wish him all the best," said Simeone, the current boss of Atletico Madrid.
"He will have success in whatever he does because he is a very capable and intelligent guy."
Simeone was involved in arguably the most controversial incident of Beckham's career at the 1998 World Cup in France.
Beckham was sent off for kicking out at Simeone in a loss to Argentina that saw England exit the tournament and led to the then Manchester United star briefly becoming a hate figure back home.
The bad blood continued four years later when Simeone tried to put Beckham off by offering his hand to the midfielder before he took a penalty in another World Cup clash. Beckham kept his focus to score the game's only goal.