The business was owned by John and Karen Blisard and began operating in 2007.
It now has five branches: two in Belfast, two in Dublin and one in Galway.
The firm's last set of abbreviated accounts suggest it made a profit of around Â£300,000 in 2014. It has been taken over by Belfast brothers David and Andrew Maxwell.
They are backed by the Dublin-based investment firm Renatus Capital Partners
Andrew Maxwell is a former professional rugby player with Ulster.
David has previously run restaurants in Arizona where he said he "fell in love with Mexican food and culture".
He said they planned to expand the chain.
"The management and crew at Boojum provide exceptional service which has been pivotal to the success of the business," they said.
"Our aim, in partnership with Renatus, is to preserve that success and build on it.
"We expect to create many new jobs as we bring the Boojum experience to new communities."
The deal was initiated by the Belfast-based corporate advisors HNH Group.
Matt McCullough from HNH played rugby at Ulster with Andrew Maxwell.
He said: "Knowing the Maxwells, who are high quality operators with a passion for Mexican food, we felt they would be capable of maintaining everything that is good about the Boojum brand, whilst moving the business forward.
"These aspects were key to making this deal happen."
The sale does not include the Blisard's barbecue restaurant, Bubbacue.
Boojum, the Belfast-based chain of burrito restaurants, has been sold.