The 34-year-old has made over 550 career appearances and could make his debut for the R’s in their Championship opener at his former club Charlton on Saturday.
Konchesky has been capped twice by England during a lengthy career in which he has also represented West Ham, Fulham and Liverpool, among others.
He was a key figure at Leicester when they won promotion to the Premier League in 2014 and then helped them to remain in the top flight last season.
QPR boss Chris Ramsey told the club’s website: “I’m really pleased we’ve managed to get Paul in ahead of Saturday.
“Left-back is an area we’re light on in terms of numbers at the moment, owing to a couple of injuries, so Paul will come in and compete for the shirt immediately.
“He’s got years of experience playing in both the Premier League and the Championship, and he’ll come in and add that knowledge and know-how, as well as his undoubted defensive qualities, to the group.”
Konchesky said: “I know what QPR as a club are all about, having played here over the years. The fans demand 100 per cent and that’s what I give every time I step on to the pitch.
“I can’t wait to get going and help this club bounce back from last season’s relegation.”
And QPR Director of Football Les Ferdinand added: “Paul is a proven performer, year on year, with a wealth of experience.
“He’s always been a physically fit player – his stats back that up – and the fact he played 29 times for Leicester last season shows he’s very much up for the challenge that lies in wait this season.
“We’re delighted to welcome him into the squad at a time when (left-backs) Yun (Suk-Young) and Armand (Traore) are both sidelined through injury. He’ll add great competition.”