Mr Putin met the Bushes at the plane, although the schedule had not called for Mr Putin meeting them at the airport.
Mr Bush flew to Sochi on Russia Airlines, which was arranged by the Russian side. The former US President was on a private trip to Russia, but changed his itinerary to meet with Mr Putin in Sochi.
As Mr Putin was opening their informal meeting at the Bocharov Ruchei residence, he stressed that Mr Bush was among the founding fathers of good Russian-US relations and that the START 1 and 2 had been elaborated with his direct participation.
Mr Putin asked his guest about the business forum he had attended in St Petersburg and said he hoped that the incumbent US President would also visit Sochi.
Mr Bush reassured his host that his son, the current US President, was a sincere friend of Mr Putin and Russia.
Russian leader remarked, in turn, that friendship and confidence mattered more than anything else, even though their opinions occasionally differed.
Mr Putin invited the Bushes for a tour around the presidential residence and grounds and for dinner.
The Bushes and those who accompanied them flew to Moscow after the meeting.