Medvedev had previously vowed to put Iskander missiles in Kaliningrad, bordering NATO members Lithuania and Poland, if Washington went ahead with the plan.
The Russian president described the US plans to replace its European missile defence project with a more flexible system following a downgrading of the long-range missile threat posed by Iran decision as "courageous."
To Russia, the now scrapped US missile shield plan was a threat to its security.
Obama's decision to drop the plan caused dismay in parts of Eastern Europe that still fear Russian interference, but was welcomed in Moscow.
A senior Russian military official said earlier this week that the military would reverse plans to deploy Iskanders after Obama's announcement.
Dealing with the issues of the US missile shield, Iran and nuclear disarmament are major elements of attempts by Medvedev and Barack Obama, the US president, to reset thorny bilateral relations that had plunged to post Cold War lows under the former Bush administration.