Taylor scored 16 goals in 76 games for Posh after signing in June 2014 for an undisclosed figure from Shrewsbury Town.
The 24-year-old Liverpool-born former Wigan Athletic trainee had a year left on his contract at London Road.
"He's a very dynamic footballer with an eye for a goal," said boss Alan Stubbs.
"The fact that we have broken our club record transfer fee just shows you what we think of Jon, and what he can bring to the football club."
The fee for Taylor surpassed the previous Rotherham transfer record, the £400,000 paid to Oldham Athletic for Jonson Clarke-Harris in September 2014.
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Rotherham United have signed Peterborough United winger Jon Taylor on a three-year deal for a club-record fee, reported to be around £500,000.