Williamson's ex-boss Colin Calderwood said: "Lee has been offered the chance to play closer to his home and to play at a higher level.
"He had one year remaining on his contract but he has the opportunity to earn himself a longer deal at Rotherham with this move."
Harford is keen to strengthen his squad further and is rumoured to be interested in Stoke City's out-of-contract forward Chris Greenacre.