Constables Craig Nicholls and Jonathan Wright were presented with the honour by the Prince of Wales at Buckingham Palace during an investiture ceremony on Thursday.
They were rewarded "for great courage" after arresting Thomas Mair, the right-wing extremist who murdered the Labour MP for Batley and Spen, West Yorkshire, in June 2016.
Mr Wright told the Press Association it was "amazing" to be given the honour, adding: "It's just day-to-day work."
On the day of the attack the two constables were on routine patrol in a police car when they heard about what had happened.
They spotted Mair roughly a mile from the scene and followed him into a cul-de-sac.
Mr Nicholls said: "He sort of gave us a look that was sinister, and then continued to walk down this cul-de-sac.
"It was a nice day and there were people out, kids in the street."
Mr Wright said: "I opened the window down and started shouting at him. Craig said he had something in his hand."
The constable told Mair to put his bag down, before the men got out of the vehicle and ran towards him.
Mr Wright said: "He then reached towards his belt and we've then taken him to the floor."
He said Mair was found with a gun, a knife, and a bag of bullets on him.
The police officers said receiving the award was "totally unexpected", and something they "never thought" they would be given.
They said they were just doing their jobs on the day of the attack, and that "you don't think about it at the time".
Bernard Kenny, who has since died, was awarded the George Medal in June for his bravery in trying to stop Mair from murdering Mrs Cox.
Mr Kenny, 79, was seriously injured when he was stabbed as he intervened in the attack.