The investment manager is believed to have donated large sums to Hearts in recent years and last year gifted the Scottish Professional Football League more than £3million to be shared equally among its clubs.
In a lengthy update to fans, Hearts chairman Ann Budge revealed Anderson would join the club's board as an independent, non-executive director on July 1.
"James is well known within Scottish football, having already significantly helped clubs at all levels to cope with the impact of the pandemic on their clubs and their communities," Budge added.
"Hearts is incredibly fortunate to have James' continued support. The value of his business acumen and his advice in driving forward the long-term ambitions of the club cannot be overstated."
Budge stressed that Hearts had secure foundations after navigating their relegation and initial challenges of the pandemic, and addressed some supporters' issues with manager Robbie Neilson.
"I know that fans, understandably, focus on on-field performances and that concerns have been expressed around our recent style of play and what that might mean for our ability to perform successfully on our return to the Premiership," she said.
"Please be assured that the board and the management team are fully aware of these concerns.
"We have done what was needed to be done to get back to where we belong and we will do everything in our power to ensure a successful return next season and beyond.
"We are wholly bought in to building a football squad that will see our youngsters playing the kind of entertaining football our supporters deserve to enjoy."
On the squad, Budge wrote: "A number of our current players are out of contract in the summer. While some have been offered new contracts and have accepted, others have decided to move on.
"There is nothing more that the club can do in these situations as the final decision always lies with the player."