Terms have been agreed between Leeds and Stoke with Sweeney due to undergo a medical next week.
The 23-year-old midfielder played under Dennis Wise at Millwall and featured in the 2004 FA Cup final against Manchester United.
The Scotsman joined The Potters in the summer of 2005 but he spent the second half of last season on loan at Yeovil. He then moved to Walsall last November, also on loan.
Sweeney played in the Saddlers' 1-1 home draw with Leeds in December, receiving a yellow card in the game.