Earlier this campaign he had a loan spell at Derby cut short by injury after just two appearances.
The Rams were keen to have Vaughan back after he returned to full fitness but their east Midlands rivals have now acquired the England Under-21 international.
Leicester are fifth in the Championship and chasing promotion back to the top flight after a six-year absence.
Vaughan is eligible for the Foxes game against Cardiff at the Walkers Stadium on Saturday, with the Welsh club just two points behind them in the table.
With leading scorer Matty Fryatt recovering from surgery after breaking his jaw in two places against Doncaster a month ago, Leicester chairman Milan Mandaric hopes Vaughan can help provide the firepower in Fryatt's absence.
"It was unfortunate to lose Matty Fryatt but James is a proper player," said Mandaric.
"It wasn't simple. The player was wanted by other teams.
"I have a good relationship with the Everton chairman and I said to him that my manager would like the player and your manager wants him to get additional experience so let's close the deal."
Leicester 11/10, Draw 12/5, Cardiff 12/5