The marriage will take place "at the end of June," said a director of Taskforce Communications, a media relations consultant to Sir James.
The spokesman was unable to say where the wedding would be held, or give any further details.
"I am afraid there is absolutely nothing more I can add at this stage," he said. "The family is not prepared to add to this statement in any way."
Khan, 42, is considered one of the world's most eligible batchelors. His fiance is 21.
An Oxford graduate and a dashing figure on the social scene during his 17 years of English county cricket, Khan now wears his country's traditional long shirt and baggy pants.
Since retiring from cricket after leading Pakistan to victory in the 1992 World Cup, he has devoted himself to a cancer hospital project in Lahore.
Khan's public statements and articles in recent months on politics and national affairs sparked speculation that he was contemplating launching himself into the national political arena.
But he denied any political ambitions while vowing to form a pressure group to serve as a check against political and administrative ills.
In March, Khan said he was considering coming out of retirement for the 1996 World Cup which will be jointly held by Pakistan, India and Sri Lanka.
Recently he spoke to the press about mariage: "At my age it's about finding the right sort of woman with the same ambitions. She doesn't have to be the same race but it would help if she was Muslim.
"I have been with some very beautiful women and admit that I had a reputation as a playboy. But my efforts are being concentrated here in Pakistan," he said.
Sir James Goldsmith made a vast fortune as one of the most cool and astute corporate raiders of his time.