The 44-year-old leaves the club lying 17th in League One, five points above the relegation zone.
Following Preston’s 3-1 loss to Yeovil on Tuesday night, Westley insisted he would not walk away from the job he has occupied for the previous 13 months.
"When things aren't working, it's my responsibility to do all I can to right them," he told BBC Radio Lancashire.
"I'm working in difficult circumstances with injuries. You've never seen me walk away from anything in my life, so don't expect me to [resign]."
Westley struggled throughout his time at Deepdale - winning just 16 of 61 games in charge - despite completely overhauled the squad during the summer, keeping just two of the crop which finished 15th the season before.