The former Hearts and Livingston manager decided against staying at the Stark’s Park club, despite a flurry of last ditch attempts to keep him and Smith at the club.
“The 60-year-old joins on a two-year deal that will see him manage Falkirk until the end of the 2023/24 season.
“The Club would like to thank Raith Rovers for their assistance in allowing John to take immediate charge of The Bairns to prepare for the beginning of the 2022/23 campaign.
McGlynn said of the move: “I’m delighted to be here. It’s been out in the public domain for a little while so it’s not exactly breaking news, but we’re delighted to be at Falkirk.
"We appreciate the task in hand, as it’s a big job and a big football club, but we’re excited at the prospect of trying to get it back where we think it should belong.”
Smith added: “I had a short spell as a player here 30 years ago, so I know how big a football club this is.
"It’s up to John and myself to push on and try to get the team back up there.”
McGlynn is also attempting to take a number of out-of-contract Raith players with him to the Falkirk Stadium, with captain Kyle Benedictus and midfielder Brad Spencer among those on expiring deals at the Championship club.
Goalkeeper Robbie Thomson and Frankie Musonda might also be tempted to drop down a division.
Falkirk ended up sixth in League 1 after a 1-1 draw against Queen’s Park ended one of the club’s worst-ever campaigns.