Kennedy's arrival does not bode well for fellow left-back Scott Griffiths, who is currently out on loan at Chesterfield.
Griffiths, who has signed from Dagenham 12 months ago, has not featured for Posh all season.
Kennedy, who goes straight into the squad for Saturday's visit of Hartlepool, started his career at Bury, where he made 143 league appearances, scoring five times.
He moved to Rochdale in 2007 and showed he still had an eye for goal, netting nine times in 132 league starts.
Three of his four Leicester appearances have come in the League Cup.
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