The bid tied a record set by a 2013 Lamborghini Aventador Roadster auctioned in March 2013 for $610,000, the statement said.
"We're truly amazed by the results of Tim Cook's remarkable donation," said Coppy Holzman, Charitybuzz chief executive and founder.
"Sincere thanks goes out to Charitybuzz's community of socially conscious bidders here in the US and overseas... we are thrilled to have amassed more than $1 million this spring for the RFK Center's powerful work."
The coffee chat with Cook was limited to two guests, who would be subject to security screening and be responsible for their own travel and accommodations.
It was the first time that Cook made his time available as part of the annual fundraising event.
The center is also raising money with other celebrity-laden offers, such as a lunch with famed filmmaker Francis Ford Coppola in California wine country, and time with actors Robert DeNiro, Alec Baldwin or William Shatner.
It plans to auction a chance to tour Space-X rocket, a day at training camp with NFL quarterback Peyton Manning and lunch with Robin Williams on the set of his next film.