The 21-year-old has impressed at Crawley since arriving on a free transfer in the summer of 2011 from Everton.
The all-action midfield enforcer impressed the Premier League club's coaching staff during the FA Cup third-round clash between the two sides and they have moved quickly to land the player.
The youngster became the Royals' second signing of the month following the arrival of Daniel Carrico from Sporting Lisbon.
Reading manager Brian McDermott said: "I'm delighted to have signed Hope, we have known all about him for a very long time.
"He has a great pedigree coming through the ranks at a top Premier League side in Everton, there were a lot of clubs in for him during this window but once he heard of our interest this was the only place he wanted to play. He's 21 and is a player we feel can play at this level.
"He's played more than 50 games for Crawley already, and any of our fans at the game on Saturday will have seen the qualities he brings, he is hungry and will be very committed to our cause.
"We're delighted to get him and I know our fans will give him every support in his time here."