The 23-year-old has penned a one-year deal at the New York Stadium following his release from Elland Road at the end of last season.
White, who came through the ranks at the West Yorkshire club, spent virtually all of the 2014/15 campaign in the treatment room with a metatarsal injury and was not offered a new deal.
His one appearance came against the Millers in the curtain-closing game of the campaign and he did enough to catch Steve Evans’ attention.
The Millers fought off a number of competitors for White’s signature and he will become their first addition of the close season on July 1, subject to Football League approval.
“It’s a big move for me. I was at Leeds for a long time but coming here was a great opportunity to get back to playing football,” White said.
“I already know a few of the lads here and I spoke to Greeny (Paul Green) and he couldn’t speak highly enough of the club so that was a big factor.”