He takes the roster spot of inside linebacker Jonas Mouton, who cleared waivers and was placed on season-ending injured reserve after tearing the ACL in his right knee last week.
Middleton spent the last four seasons with Jacksonville. He played in 10 games last year, starting three, and had 18 tackles.
Middleton gets another chance after being noticed by Chargers personnel executive Tom McConnaughey.
"You always have targets of certain players," coach Mike McCoy said. "Tom and the rest of the personnel department do a great job. And any time that we can acquire someone that can make us better, that is what we are going to try and do."
The Chargers have undergone an overhaul after missing the playoffs three straight years and posting their first losing season since 2003.
"We are going to keep churning the roster," said McCoy, a rookie head coach after serving as the Broncos' offensive coordinator. "It won't be the last time we make a transaction. We're going to keep turning the roster over until we get the 53 we want."
The Chargers figure to have three new starters in the secondary.
Where Middleton will land will be determined. But he has 100 tackles and two interceptions in 49 career games, which includes 12 starts.
"He's contributed on special teams, too, and we are looking for guys that come in that have position flexibility," McCoy said, noting Middleton's 33 special-teams tackles. "He has played inside in the nickel a little bit, here and there, but it just adds some depth to us. We'll see where he fits in as time goes along."