The American businessman last year accepted an invitation to join the club's board and on Friday his company bought 4,839 shares from members of the Carr family, including Arsenal director Richard Carr.
Carr said: "It has been a wonderful ride and the family have enjoyed every minute of it. I hope there will be many more magic moments for us in the future."
A statement on the club's official website read: "The shares were acquired at prices of £8,500 per share and £10,500 per share.
"As a result of the acquisition, Stan Kroenke has a beneficial interest in, and controls voting rights over 17,613 ordinary shares in the company, representing 28.3% of the company's issued ordinary shares."
Arsenal chairman Peter Hill-Wood said: "I would like to pay tribute to the long-standing commitment that the Carr family have shown towards Arsenal.
"The club are hugely indebted to them for the role that they have played in the development and success of the club over the years.
"The board particularly wish to thank Richard Carr for his hard work, effort and integrity since joining the board in 1981 and I am pleased to say Richard will continue on as a director of the club."