The two clubs were embroiled in a relegation battle last season, with Leicester surviving the drop and QPR slipping back into the Championship.
Konchesky is not retaining his Premier League status, with new manager Claudio Ranieri deeming him expendable.
The experienced defender could make his debut against former club Charlton at the weekend, with manager Chris Ramsey telling the club website the 34-year-old helps fill a position of need for the club.
He said: "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."
QPR fans are largely positive about the signing, realising he is a stop gap solution who could be a useful short-term fix.
Konchesky is a solid signing, just need another centre half now...— Ian Dallibar (@WholeShow) August 4, 2015
The future looks decent for us regarding left backs. Robinson/Kpecwa and possibly even Yun. Not sure why the panic over Konchesky #QPR— Norths (@NortholtRanger) August 4, 2015
Perch & konchesky - not a bad championship pair of full backs. Well done Chris & Les #QPR— Brad woodbridge (@bwoodbridge33) August 4, 2015
Not sure what's wrong with the Konchesky signing - yes, #QPR appear to have a few left backs, but they all appear to be injured.— Nick Reinis (@nickreinis) August 4, 2015
Konchesky deal come out of no were great loan signing #QPR— David QPR Allen (@David_allen17) August 4, 2015
Happy with Konchesky. Steady, experienced Championship player. Exactly what we need. Plus no more Clint Hill at left back #QPR— James Smith (@SmudgeQPR) August 4, 2015
Leicester City fans however offer a different slant on the Konchesky deal, expressing delight that the former Fulham and Liverpool defender has been moved on.
He had been at the Foxes since 2011, making 26 Premier League appearances last season, reaction on social media indicates that everybody is a winner out of this particular deal...
Best bit of transfer business Leicester have done so far is sending konchesky out on loan.. Unlucky QPR— steve southern (@TheRealSteveSuv) August 4, 2015
Might run into the garden, launch a wild lunge into a tree and smash in a celebratory own goal in tribute to Paul Konchesky's #lcfc career.— James Knight (@MFoxx2) August 4, 2015