Midfielder Reed, who towards the end of last season had a loan spell at Albion's League Two rivals York, joins the Brewers on a one-year deal after being released from Premier League club Sunderland where the 22-year-old had been a regular in the Black Cats' development squad.
MacDonald, 23, has signed a two-year contract after impressing during a 17-game loan spell at the Pirelli Stadium from Burnley last season.
Striker Knowles completes the trio of arrivals. The 21-year old, who scored 10 goals in 14 appearances for Harrogate Town last season, has been rewarded with a year-long deal after spending the final few weeks of the last campaign with Gary Rowett's side.
Rowett said: "I'm delighted to be bringing in three young, enthusiastic and talented individuals who all want to be a part of Burton Albion Football Club.
"Adam is a midfielder who arrives with good pedigree and is exactly the type of player and personality we want at the club and we're very pleased to add him to the squad.
"Alex came in last season and did very well for us and I think he is only going to get better. He's a good age, has plenty of ability and knows exactly what we're all about and what we want to achieve.
"Dominic is an exciting prospect who clearly knows where the back of the net is and deserves his chance at professional level; his attitude during the brief time he spent with us was spot on."