"Just landed in Moscow. Beautiful day. Can't wait to see Pres Medvedev @KremlinRussia_e," Schwarzenegger wrote on his Twitter micro-blog, including a link to a photo of himself with a cigar in the back of a car.
"@Schwarzenegger, welcome to Moscow. Looking forward to meeting you and your delegation at @skolkovo," the Russian president responded on his Twitter site.
Schwarzenegger is leading a delegation of top Silicon Valley executives and venture capitalists to Russia to discuss investment opportunities in Russia's high-tech sector. The trip includes a stop at Skolkovo, the site of the high-tech research hub Russia is creating near Moscow.
The center has been dubbed Russia's Silicon Valley and Medvedev is keen to bring in U.S. know-how to spark the project.
He has made modernization the center of his economic policy agenda and visited Silicon Valley during his visit to the United States in June.
The president also met the California governor during the trip.
As well as exchanging tweets, the president and the governor started following each other on Twitter.
Twitter.com is a micro-blogging system that allows users to post short messages (up to 140 characters) and send them to other Twitter users. The messages are known as "tweets."
