The midfielder, who joined Crawley from Everton in 2011, has agreed a three-and-a-half year contract.
Reading manager Brian McDermott told the club website: "I'm delighted to have signed Hope, we have known all about him for a very long time."
McDermott added: "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."
Akpan played for the second half of the Royals' friendly win over QPR on Tuesday.
Reading said the deal is subject to final ratification of all the paperwork from the football authorities, but they expect that to be a formality.