The animosity has been lingering since Beckham was sent off at France 98 for kicking out at Simeone.
Many felt Simeone overreacted, leading to a media-fuelled feud between the two.
Beckham finally exorcised the ghost by scoring the goal that lifted England to a 1-0 win over Argentina at this summer`s World Cup.
The England skipper ignored Simeone`s antics before taking the penalty, the Argentine tried to shake his hand, and embraced his adversary after the match was over.
Beckham has now revealed the spat is over, claiming Simeone acted like a 'gentleman' after the match.
Speaking to the Sun, Beckham said: "Simeone tried a few mind games to put me off before I took that penalty, but I expected that. It is all part of football.
"But then he showed me what a gentleman he is by coming up to me at half-time and then again at the end of the game and shaking my hand.
"Even though he was desperately disappointed because Argentina had lost, he said to me 'Good luck for the rest of the tournament'.
"I could tell it was a genuine gesture.
"I have always said he is a great player and he, in return, said I am quite good too.
"Now we have a healthy respect for each other.
"I've been asked countless times if I have forgotten what he did in France 98. You have to forgive and forget.
"There is no lingering grudge between us - just mutual respect between people who regard each other as good players and professionals."
