The former Manchester United centre-back, who helped the club to the treble in 1999 during his time at Old Trafford, will take charge of the Royals in his first permanent managerial role following previous stints as assistant at Zwolle and Ajax.
The Dutchman succeeds Brian McDermott at the Madejski Stadium after his second stint in charge of the club lasted just six months before his sacking at the end of the 2015-16 campaign.
"I am delighted to welcome Jaap to Reading. He was the first choice amongst a vast number of applicants interested in the position and we are thrilled that we have managed to secure the signature of a manager with such an abundance of experience," chief executive Nigel Howe told the club's official website.
"His record as both a player and coach, at the very highest level in England, Italy and Holland as well as internationally, speaks for itself and on behalf of everyone at Reading Football Club I would like to wish Jaap the very best in his career as a Royal."