Jamaica international Williamson, 34, who will join on 1 August, has signed a 12-month deal after making 66 starts in three years at Blackburn.
Dyer, 33, has agreed a similar deal, having spent the final three months of last season with Burnley.
Delaney, 19, arrives from Irish club Wexford Youths on a two-year deal.
And the club have an option to extend his contract by a further year.
Williamson came through the Mansfield youth system and his previous clubs also include Northampton, Rotherham, Watford, Sheffield United and Portsmouth.
Burton manager Nigel Clough said: "Lee is a vastly experienced midfielder in the Championship and is the second international who's joined us in the last 10 days - quite something for Burton Albion."
Dyer most successful spell came during six years with Leicester City, helping the Foxes to promotion from League One and the Championship - during which he also captained the side.
"I think his experience will be vital for us this season," said Clough.
"We are a little bit short in wide areas and Lloyd will provide that outlet, especially if we are under the cosh. His pace is also going to be an asset."
Teenager Delaney will be playing in England for the first time and Clough added: "He can play left-back or left centre-half. He hasn't yet played at a decent level but he does a lot of things naturally.
"He has not been in full-time training which means he's been blowing a bit in the last 20 minutes of games but we think we can get him up to speed."
Burton Albion have signed midfielder Lee Williamson, winger Lloyd Dyer and defender Ryan Delaney after all three spent pre-season with the club.