The Pumas hooker is the third-most capped Argentina international.
It will be his swansong, and he has brought his family to New Zealand to share it with him.
"It is a joy for me to be here in New Zealand and it brings me a lot of happiness and is a privilege to be playing in my fourth World Cup," he said. "I am very proud.
"It doesn't get any easier. It will be even more difficult than the other three, especially physically.
"But it is easier for me to enjoy every moment knowing that it is the last one."
Ledesma (38) has been playing first-class rugby for 21 years and played his first test for Argentina against Uruguay in 1996.
He played a key role in Argentina's best World Cup performance in 2007 when it beat France 34-10 to finish third.
Playing a World Cup in New Zealand is special to him.
"The country of rugby is New Zealand," he said.
There is a lot of interest in the Pumas' performance in the World Cup back in Argentina and a lot of people will be watching games on television.
"There has been a lot of interest in us over the last four years," Ledesma said.
"A lot of people will be getting up at 5.30am in the morning to watch our games.
"They are expecting a lot from us and expecting the same results as the last World Cup."
He knows that it will be a difficult task to beat England at the Otago Stadium tonight.
"They are the favourites," he said. "They are ahead of us physically, technically, tactically.
"They have just won the Six Nations and have dangerous players everywhere. I don't know if we will beat England but we can."
Historically and culturally Argentina has always had a strong pack but its backline has not been up to the same standard.
"Everything points to England winning by 30 points and I hope they feel that way," Ledesma said.
The odds are stacked against Argentina because they have only had one test in the past 11 months.
"In the last four years we have played only 18 tests and England has played 42," Ledesma said.
"They won 80% of their games and we only won 30%. They go in as the favourites.
"It is very difficult for us but it has been like that for ages. It is the reality and we can't deny it. We will just have to cope with it and do our best.
"We would have preferred to play a couple of games against the better teams over the last two months."
The lack of international games had been a big problem for Argentina rugby but it will be helped next year when it joins southern hemisphere teams South Africa, Australia and the All Blacks in the Four Nations competition. Argentina has overcome these problems in past World Cups.
"We have done it in the past but we can't keep thinking about the past," he said. "We have to do it tomorrow."
Argentina's best chance of reaching the quarterfinal is to beat Scotland in its third game. By that time it should have gelled into an efficient unit.
"We have only had one hard game of rugby against Wales so it is difficult to know where we are," Ledesma said.