Kurtis Dilks, 35, was also ordered to serve an extended licence period of five years by a judge at Nottingham Crown Court who said the former Chelsea and Arsenal defender and his partner Sharon Canu had suffered psychological impacts that "cannot be overstated".
The judge said the attack on the footballer's Surrey home was "extremely terrifying", and he described the gang as "intelligent, violent and chillingly ruthless men".
Dilks was the only one of the gang responsible for the robbery to be caught after his DNA was recovered on the cable ties used to restrain Cole and Ms Canu.
In an impact statement read to the court earlier, Cole said the "terror and confusion" on his children's faces when the gang smashed into his home "will never leave" him.
He added: "These images and thoughts will never ever leave my mind and can pop up any time."
Ms Canu was in court on Friday to hear her statement also being read by prosecutor Michael Brady QC.
The trio were also convicted of being part of the theft of a £3.5m tiara worn to the coronation of Edward VII from the Harley Gallery on the Welbeck Estate in Worksop, Nottinghamshire, in 2018.