A member of Robbie's family is quoted by the Daily Star newspaper as saying: "Rob is very fond of Gary and considers him a solid rock in his life.
"Mark was always one of his fun time pals, but Rob really wants to thank Gary and show his respect for their special bond."
Robbie's long-time best friend Jonathan Wilkes will also act as a best man at the 36-year-old pop star's wedding.
The former Take That bandmates had a high-profile feud following Robbie's departure from the group in 1995.
However, in recent years the pair have patched up their differences and it is believed at some point Robbie will rejoin Take That.
He recently said: "It will happen - but not in the next two years. There are contracts to fulfil, then I can do what I want."