During an address to the students at their certificate presentation ceremony, Harry told them that supporting the four-day Games would be the "most amazing weekends of your lives".
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The teenagers have been trained by Facebook in how to use social media to promote the sporting event, which will be held in capital from September 10-14.
"We're very short on time, it's going to happen; what are we - a month and a half away from the actual Games?" Harry told the youngsters who had all gathered at Bethnal Green Academy in East London on Monday to meet the Prince.
"The more noise and the more enthusiasm you guys can get behind the Invictus Games, get your friends involved, buy some tickets, come down and scream and shout - I promise you, you will not regret it, it will be the most amazing weekend of your lives."
In May, Harry sent his first ever tweet as he officially launched ticket sales for the Invictus Games. The Prince was asked to mark the occasion by posting a tweet from the Invictus Games' account.
But speaking to the students on Monday he said: "It is very hard for me to tweet about the Invictus Games or tweet about something that means a lot to me whereas at the same time I really quite hate Twitter by the invasion of privacy - I think you all understand what I'm talking about.
"So I would love to tweet about things I care about, on a regular basis - if people wanted to hear about it, that would be good."
Prince Harry addresses The Invictus Games digital champions
The Invictus Games are a paralympic-style sporting event for injured servicemen and women. The 29-year-old Prince came up with the idea for the games after attending the US version, the Warrior Games, in Colorado last year.
The Games will see 300 competitors from around the world take part in events, which could include shooting, sitting volleyball, track and field and wheelchair basketball.
The aim of Harry's project is to encourage wounded servicemen to stay physically active when they return to their local communities and to introduce them to sporting challenges on a Paralympic leve