The right-sided, attacking midfielder was earlier released by former Club Sheffield United, with the Reds quick to snap up his signature as a free agent.
The 20-year-old has penned an 18-month deal with the Reds - running up until June 2017.
Manchester-born Khan spent a successful trial with the Reds last week, with Head Coach Lee Johnson saying:
"Otis did really well in his trial arranged by our recruitment team and we're pleased he's joined us.
"He excelled at Conference level recently with Barrow and this is a great opportunity for him to kickstart his career."
A former Manchester United scholar, Khan has been handed squad number 19 at Oakwell.
"I'm really happy to sign. It's a really young squad and I'm happy to have the chance. I'm over the moon to be here.
"I'd say I'm an attacking midfielder who likes to create and score goals. I want to create opportunities for players and myself."
