The 27-year-old has not featured for Darren Ferguson's men since their 5-2 thrashing at Burnley in September and could make his Millers debut in Saturday's League Two clash at Aldershot.
"We spent a long time this week getting the deal done and we are delighted to have Lee here", said boss Steve Evans.
"We tied the deal up late on Thursday night and he's signed which is great news. Lee is a great lad, he is an attacking midfielder who likes to get into the box and I think our fans will love him.
"We are only talking less than 18 months ago that some clubs bid £700,000 for his services so he comes here with a lot to prove but he wanted to come and he wanted to play so I didn't really need to sell it to him."