The event pits America against an international team, that excludes Europe, at Liberty National Golf Club in New Jersey from 26 September.
"It is a great honour for me to be even a small part of the Presidents Cup," said Trump, who said he has watched the tournament since it began in 1994.
"It gets better with age. This will be the greatest of them all."
PGA Tour commissioner Jay Monahan said organisers look forward to Trump being involved "in any capacity his schedule allows".
Former American president Barack Obama twice performed the role as honorary chairman during his term in office.
American president Donald Trump has accepted an invitation to be honorary chairman of golf's Presidents Cup.