"I am absolutely delighted to get him back into the football club," manager Brian Laws told BBC Radio Lancashire.
"There's been a number of clubs courting him this summer but we've got a great player on our hands."
Cork made 11 appearances for Burnley last season in his first spell with the club, scoring his only goal in the 4-2 win over Tottenham on the final day of the campaign.
But following the Clarets' relegation from the Premier League Cork returned to parent-club Chelsea.
Over the moon, helps with the loss of McCann big time. If Cork produces the sort of form and attitude he showed last season he will be an awesome signing Beefc Although he has still to make a first-team appearance for the London side since joining as a trainee in 2006, Cork has had loan spells with a number of clubs before moving to Turf Moor in February.
"We know he's a good quality player," said Laws. "He's hungry and had a great experience with us last year.
"It's been the main objective for us to try and get him in as soon as we possibly can, although it's been a very long process. We've had to be very patient because Jack's tasted the Premier League and we knew that if any club came in for him we'd have no chance.
Laws admitted he would have been interested in bringing the England U21 international to Turf Moor even if Chris McCann had been fit.
"We're not just talking about the short-term, but the long-term future as well," he said. "Jack's one of those players that he's such a young age that there's plenty more to come and we'd like to have a piece of that.
"We decided to just step back and speak to Jack on a regular basis and keep us informed. But now we've got a decision where we could no longer hold out on Chris [McCann] because of the surgery required the timing is right to bring him back."
There will be full commentary on BBC Radio Lancashire on Ipswich v Burnley from 1500 BST on Saturday.