The 35-year-old had a brief spell at Kenilworth Road in the 2007-08 season as after joining from the Shrews, he played 26 times, scoring four goals, sold to Wolverhampton Wanderers for £675,000 with the club in financial difficulties.
Edwards went on to feature for Reading and then Shrewsbury again, also winning 43 caps for Wales, as Bala manager Colin Caton said: "It’s great to have Dave Edwards on board, he’s an unbelievable signing and an unbelievable capture for the club..
"I spoke to Dave on a couple of occasions, we had a couple of good chats but I never thought he’d be interested in the Cymru Premier.
“To get him on board is absolutely fantastic.
"He was a pleasure to deal with, and he’s going to add so much to us as a player, as a person, and his knowledge, and his experience around the dressing room is going to be second to none."
Former Town defender Lloyd Jones has moved to League One Cambridge United on a two year deal after rejecting a new contract at Northampton Town.
The 25-year-old, who made 14 appearances for Luton, scoring once, between 2018-20, had been a regular for the Cobblers as they were relegated to League Two last term.
On heading to the Abbey Stadium, Jones said: "I met the manager a couple of weeks ago and I really liked what he had to say and the way he plays football.
"It is going to be a proper fresh start for me and I can’t wait to go.”
U's head coach Mark Bonner added: "He is an excellent shape and size, handles the ball well and is mobile.
"This gives Lloyd an opportunity to settle in the area and find some stability in his career.
"Having experienced League One football and with his best years ahead of him, we are expecting him to use his previous experiences to add real value to the team, and to realise his undoubted potential."
Meanwhile, one-time Hatters midfielder Dean Brennan has become head of football at National League side Barnet, with the Bees appointing former Crawley, Oldham and Notts County manager, plus ex-Liverpool and Leeds United winger Harry Kewell as head coach.
The 40-year-old joined Luton in 2000, playing 14 times and scoring once for the Hatters, until spells in non-league for the likes of Hitchin, Dunstable and Barton, while he has also managed Hemel Hempstead, Kingstonian, Billericay and Wealdstone.
Brennan said: "We want to bring success back to the football club but that has to start with honest hard work.
"We need to bring everyone together, that includes the supporters, they are the life and soul of the club, so let’s all get together and move forwards as one.
"We have lots of recruitment to do and that works starts immediately, I will be tasked with bringing the very best players who want to work hard for our club."