Reports earlier in the season suggested the teenager had rejected a new contract offer, along with fellow youngster Danny Wilson, because they wanted a lucrative move to England.
But boss Walter Smith later revealed there had been a misunderstanding in Fleck's case and that he was keen to remain at the Scottish champions.
Speaking to the club's official website Fleck said: "I'm delighted to get everything done and dusted and now it's a chance for me to concentrate on my football.
"Talks have been going on for a few weeks now and some things were written about me looking to move on but I have always wanted to stay with Rangers.
"It's great for me that I've got my future sorted out. I'm still only 18 and to be getting a chance to play for a club like this is fantastic at my age.
"I've been getting a few opportunities to play in games and come off the bench and that can only help me in the future.
"In the long term, I hope to keep developing as a player and I don't believe there is anywhere better for me to do that than here.
"More immediately, I'm desperate to help the team retain the league title over the next few weeks.
"We are in a good position in the SPL table but although a lot of people are saying the championship is already won, we have a bit to go yet before that's the case.
"Celtic could still come back and make things hard for us so we are all concentrating on making sure that doesn't happen.
"Personally, getting my future resolved allows me to focus totally on what we need to do and I'm ready to play my part between now and the summer."
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