Topics such as the economy and public policy were on the agenda during their discussions.
The two men then visited the nearby Wellington Barracks and met soldiers from the 1st Battalion the Grenadier Guards who earlier this year returned from a six-month tour in Helmand Province, Afghanistan.
See pictures of the visit on Flickr
Speaking in front of about 300 troops, Mr Schwarzenegger told them they were the “true action heroes” and paid tribute to the UK armed forces for being “great partners” with the US.
He said:
I get hailed a lot of times when I travel around the world as being the action hero. But I know the difference between a movie action hero who is make-believe and the true action heroes. You all are the true action heroes because you are risking your life. You are risking your life every day when you go out to the front so I say thank you, thank you, thank you for the great work that you are doing.