Reach was scheduled to return to Middlesbrough after the weekend defeat at Shrewsbury after the deal was extended in February, but the 21-year-old will now stay at Bradford until after the Easter Monday game at Swindon.
"It is obviously good news for us to see Adam staying with the club," City boss Phil Parkinson told the club's official website.
"He has been an excellent acquisition for us and we've enjoyed working with him so far.
"Adam is really enjoying his football here and we're delighted to keep him with us."
Reach has made 11 appearances for Parkinson's side, scoring one goal, since first arriving in January following a two-month loan spell at Shrewsbury.