The 36-year-old, who had overseen the club's ‘B’ team, takes up the post vacated by Ibrox legend Barry Ferguson who moved to Alloa Athletic.
Kelty won promotion to League Two on Sunday, defeating Brechin City over two legs in the Pyramid Play-off final.
On Twitter, Thomson admitted he left Rangers, where he played with distinction between 2007 and 2010, with a “heavy heart” but noted that he is sure he "will be back”.
He tweeted: “With a heavy heart I left the club today - can’t tell you how much I’ve loved working and representing you all. Special club, and I’m sure I will be back. New challenge, new start....let’s go Kelty.”
It is Thomson’s first step in a first-team management role believes it is the “perfect fit” at this stage in his managerial career.
“It’s a club that I know well and I am sure we can achieve success together in the years ahead,” he told the club’s website.
“I can’t wait to get started on the challenge ahead in my first managerial job in the SPFL and to get to work with the players and backroom team on the training pitch, I am also really looking forward to meeting the Kelty Hearts supporters and people within the community over the coming weeks and months.”
‘Drive and ambition’
Thomson, who set up his own football academy, is held in high regard for his coaching ability, one of the key reasons Kelty were attracted to him.
The club's general manager Dean Mckenzie said: “You can’t help to be impressed with his drive and ambition, we are thrilled he chose Kelty Hearts FC to begin his managerial career and to have one of the best up and coming coaches at our club.
“We have no doubts Kevin will go onto bigger things in his management career and we hope to help him do that by giving our new manager and his team our full backing.”
Meanwhile, Rangers will field a ‘B' team in next season's Lowland League after it was confirmed at the division’s AGM.