Stuart Pearce's squad for the tournament features five Welshmen despite the opposition of the Football Association of Wales, who fear for the continued independence of their own national team.
Veteran Manchester United and Wales midfielder Ryan Giggs has been made captain and will be joined by fellow countrymen Joe Allen, Neil Taylor and Craig Bellamy, in addition to Ramsey.
"I hope all our home fans will come together for this occasion," Ramsey told the Daily Star. "They need to get behind the England lads in Team GB as well because this is a real one-off.
"For us Welsh players it hasn't really been a battle to win over the fans because, hopefully, they understand our point of view about playing in the Olympics.
"It is very important to me and, to be honest, we're old enough and mature enough to make our own decisions.
"We're being offered a once-in-a-lifetime opportunity, one too good to turn down and we all want to be remembered for the part we play."
Wales have failed to qualify for a major tournament since the 1958 World Cup in Sweden, preventing the likes of Giggs, Mark Hughes and Ian Rush from appearing at the finals of an international competition.
Ramsey believes that the experience gained by the younger members of the Welsh contingent representing Team GB will aid them in the their bid to qualify for the 2014 World Cup in Brazil.
"This is a fantastic experience for all the players and, from a Welsh point of view, it'll be the first tournament we go to - but not the last," the 21-year-old said.
"I'd like to do more with Wales. We have come on so much since Gary Speed was our manager when the team was playing some fantastic stuff.
"The rankings show just how far - we are up to 38th now. At one point we were about 120th!
"New manager Chris Coleman is a believer in the style that Gary introduced as well and now we want to have a very good World Cup qualifying campaign and make it to Brazil."