Lee and David have initially penned contracts until the end of the current season.
The club revealed the board of directors have been highly impressed with the work of the pair to date and have “full confidence” in them as a coaching team to deliver the ultimate aim of promotion back to the Ladbrokes Championship.
Lex Miller, interim chairman, said: “The board have been very impressed with Lee and David since their return to the club. Their drive and ambition to bring success to this club shines through each day and we fully believe they can lead us to promotion this season.
“There is no denying the lift that Lee and David’s presence has given both internally and externally to the club and we hope this continues, starting tomorrow at home to Raith Rovers.”
Lee Miller said: “Today is a dream come true. To officially lead this club has been a long-term ambition of mine and I can’t think of anyone better than David to be in this role with.
“We have always believed we are the right people to help build the club back up to where it should be and we are delighted to have the opportunity to do so. The support of everyone at the club and the fans has been overwhelming, we can’t wait to get back to the Falkirk Stadium tomorrow.”
David McCracken added: “This is an extremely proud day for myself and Lee. We have enjoyed every second of the last few weeks and are determined to bring success to the club.
“The squad have been really good in training, we have a great group of players and myself and Lee are looking forward to working with them each day to improve and deliver results.
“We are really looking forward to tomorrow and hope to see a huge turnout from the fans, their support has been magnificent and I hope that we can start our tenure with three points for them.”