Gatland, who worked as the 65-year-old's assistant in 2009, was named as the Lions coach on Tuesday.
"Warren was brilliant in South Africa in 2009 - I can't say enough about him," said McGeechan. "He understands the Lions ethos and has huge respect for it.
"He was a brilliant assistant coach three years ago, but he knows all about being the number one guy after so many years in that position with Connacht, Ireland, London Wasps and Wales.
"He was always the outstanding candidate for the top job in Australia next year. He has a great rugby brain and he is a good man manager."
McGeechan further elaborated on the 48-year-old's abilities as a coach.
"The other great thing about Gats is that he shares things and is prepared to put everything out there on the table," he said. "He gets huge respect from the players for that.
"He has the ability to pull players together. He has coached in Ireland, England and Wales and he has always taken on board the strengths and ideas from those countries.
"He has become used to working with players from different countries over the past 14 or so years and has always learned along the way. That's such a critical issue with the Lions."
Graham Rowntree and Shaun Edwards are expected to be made Gatland's assistants, but those appointments will not be announced until October.