The 28-year-old, who was released by Wigan in June, joined Burnley on their pre-season tour of Ireland.
He has agreed a three-year deal and is expected to be involved in the Sky Live Championship opener against Bolton on Saturday lunchtime.
"There were a few clubs in for David, but he wanted to get a feel for us," Burnley manager Sean Dyche told the club website. "Geographically, he is not a million miles away, so that helped.
"He came in a couple of weeks late, but he is a very fit lad and we managed to accelerate him into the group, so we are looking forward to how he progresses here."
"I just felt this was a very good option for me at this stage of my career," said Jones.
"I was a free agent and I was listening to various options that were coming available, but after meeting the gaffer I was happy to join and I have been very impressed."