The combative midfielder joins Lee Johnson's rejuvenated Reds after the two Clubs agreed an undisclosed fee.
The 20-year-old has penned a deal which runs until the end of the season, with an option to extend to the summer of 2017.
Speaking to Barnsley PlayerHD after signing, Jak said,"I'm delighted to join Barnsley. It's a massive Club and I can't wait to get started.
"I want to help the Club get to where it wants to be.
"I like tough tackling and to get on the ball and play football, so hopefully I can get started soon."
The Liverpool-born midfielder will wear squad number 12 with the Reds set to face Swindon tomorrow at the County Ground.
