Ms Kirkby, who took over in February, plans to double cash flow over the next five years, slash £3bn of costs and boost the dividend. The announcement of the new strategy last month triggered the company’s biggest one-day share price increase for 24 years.
New Street Research analyst James Ratzer described Mr Slim’s investment as a “vote of confidence”.
Shares in BT rose 1pc after the shareholding, made through the billionaire’s vehicle Inbura, was revealed in a stock market filing.
A BT spokesman said: “We welcome any investor who recognises the long-term value of our business. We have frequent communication with all of our shareholders and meet with major investors on a regular basis. We look forward to engaging with Inbursa, just as we do with all investors.”
Previously the world’s richest man, Mr Slim controls America Movil, the largest mobile phone operator in Latin America. The businessman also has interests in banking, energy and construction.
A fine art lover with a fondness for cigars, Mr Slim’s business interests are chiefly in the Americas but he has also made forays into Europe.
He also owns a significant chunk of Telekom Austria and is the group’s largest shareholder through America Movil.
Mr Ratzer said: “Slim’s track record in European telecoms is mixed and arguably without any clear industrial strategy, other than trying to pick up assets he thinks are cheap.”
He added that Mr Slim’s presence on BT’s share register would likely be welcomed as it would help to balance out the influence of other significant shareholders.
“For BT, having a new angle in play can only help. There might even be a chance that Slim has bought some of these shares from Drahi.”
Mr Barford said the Mexican tycoon may have been attracted to the potential payouts on offer from BT.
The roll-out of fibre broadband has restrained BT’s ability to pay large dividends for many years but this project is scheduled to end in 2026. Many investors see potential for BT to start paying out more cash once it is concluded.
Mr Barford said: “You can see the appeal of BT to a long term investor.”
It comes as overseas investors circle UK telecom companies, many of which are valued more cheaply than peers elsewhere.
United Arab Emirates-based telecoms group e& recently acquired a 14pc in Vodafone, while Xavier Niel, the French billionaire founder of Iliad, also owns 2.5pc in the group.
Mr Slim was the world’s richest man between 2010 and 2013, and is currently the 17th wealthiest person on earth, according to Bloomberg.
A fanatical baseball fan who supports the New York Yankees, Mr Slim is also a financial backer for Formula One driver Sergio Perez.