The Royal and Ancient invited champions to play the first, second, 17th and 18th holes at the Old Course on July 14.
Ballesteros, who is a two-time Masters Tournament champion, is recovering from a brain tumor. R&A director of championships David Hill said Monday that he hopes "the majority of our former champions will accept the invitation."
The BBC will broadcast the two-hour Open Champions' Challenge, and the winners will receive prize money for a charity of their choice.
EUROPEAN PGA TOUR: The 2010 schedule will feature 47 tournaments that will contribute to the second Race To Dubai title.
Not included next year are the European Open, the Madrid Masters and the Indonesian Open because of the global economic downturn.
A three-week delay in announcing the schedule had led to speculation that the Race to Dubai, with its $30 million prize money, might not be included after Dubai construction giant Nakheel announced it was struggling to refinance debts of $26 billion.
European golf's governing body said Monday that the second edition of the Dubai World Championship would go ahead with the same prize money as 2009.
ASIAN TOUR: The PGA Tour reached a multiyear deal with the Asian Tour to stage the Malaysia Asia Pacific Golf Classic.
The tours said the event will be played late next year at The Mines Resort and Golf Club, with the winner receiving $1 million from the $6 million purse.