Cork, 21, enjoyed a successful four-month loan spell at Turf Moor last season and scored his first Premier League goal in the win against Tottenham on the final day of the campaign.
A statement on the club's official website said: "The 21-year-old was an outstanding success in his four-month stay as a Claret, making 11 appearances, with his influence on the field matched by his popularity in the dressing room."
The England under-21 international has had previous loan spells with Coventry, Scunthorpe, Southampton and Bournemouth, clocking up over 100 league appearances.
After beating off competition from several other clubs to secure his signature, boss Brian Laws said: "I'm absolutely delighted to get Jack back into the club.
"He's a good quality player, he's hungry and he's a great lad in and around the club. There have been a lot of clubs courting him this summer so the fact we have got him and the timing of it couldn't have been better."
Meanwhile, Laws has stressed that Chris McCann's six-month injury absence with a knee injury will not affect future contract talks.
McCann's current deal expires at the end of the season but Laws said: "Chris is in the last year of his contract and this (the injury) will not impact on our decisions. We expect him to make a full recovery and all it has done is put his career back 12 months."