Georgia has abolished visas, so Russians can visit freely. Everyone arriving at the Tbilisi airport is welcomed at passport control with a small bottle of Georgian wine.
Natela Baguashvili, 47, who owns a small food shop in Tbilisi, remembers how strange it was for her and her Russian friends to find themselves on opposite sides during the war.
"I grew up with Russian friends and classmates, and we have stayed friends and we write back and forth," she said. "During the war they were worried about us. They love Georgia."
The Russian government has welcomed Ivanishvili's victory. Foreign Ministry spokesman Alexander Lukashevich said Wednesday that Moscow hopes Georgia will now be able to establish "constructive and respectful ties with its neighbors."
The head of the Russian parliamentary committee in charge of relations with former Soviet nations said there is hope for more positive relations. "Historically, geographically and culturally, our people are simply bound to have good-neighborly relations," said Leonid Slutsky.
Ivanishvili has strong business ties in Russia, and the Kremlin may be hoping to use him to bring Georgia back into the fold. Saakashvili has accused him of being a Kremlin stooge.
Ivanishvili denies this, and since his Georgian Dream coalition won the election, he has used every opportunity to reaffirm his commitment to making Georgia an integral part of Europe and a member of NATO.
NATO chief Anders Fogh Rasmussen reciprocated on Wednesday. "NATO is committed to our close relationship with Georgia and we look forward to making this relationship even stronger," Rasmussen said in a statement.
Ivanishvili took pains Wednesday to show his distance from Moscow.
"I have not received congratulations from Russia and have not contacted the Russian side," he said. "And moreover I am going to the U.S., to our main partner and friend."
Ivanishvili said he had an official invitation to visit Washington, but would wait to schedule a visit until after the U.S. presidential election in November.
He will become prime minister after the new parliament goes into session on Oct. 21.
Isachenkov reported from Moscow. Misha Dzhindzhikhashvili in Tbilisi, Georgia contributed reporting.