Striker Symes and centre-half Sharps join permanently after successful loan spells last season while the versatile Edwards arrives at the Pirelli Stadium having left Rochdale this summer.
All three players have put pen to paper on one-year deals.
Following the signing of left-back Chris Hussey on Friday, the trio take Albion's number of new faces this summer up to six.
Manager Gary Rowett told the club's official website: "I'm delighted to have Phil, Michael and Ian on board and it is pleasing to now see the squad taking shape.
"It was important to keep the nucleus of the side together and in that respect it's great to have Michael and Ian back with us permanently. They have plenty of experience, know what the club is all about and in both cases have expressed a real desire to come back here and help the side kick on next season.
"In Phil we have a player who knows what it takes to be successful at this level as well as the league above and he is a very consistent performer.
"I always remembered he played very well against us for Accrington. He's someone who will give us great versatility and add further competition.
"At 27 he's also at a good age to continue progressing and I'm sure he'll prove to be a big asset to the club."