An announcement by Foreign Affairs Committee member Vyacheslav Nikonov that Mr Trump had triumphed was almost drowned out by clapping and cheering in the State Duma.
State news agency RIA-Novosti and Russian website Interfax.com quoted Mr Nikonov, also chairman of the Education Committee, as saying: "Three minutes ago, Hillary Clinton acknowledged her defeat in the US presidential elections and just seconds ago, Trump began his speech as president-elect. I congratulate all of you on this."
President Vladimir Putin subsequently sent 70-year-old Mr Trump a telegram congratulating him on the outcome.
In a brief statement, the Kremlin said Mr Putin had expressed his hope that the pair could "work together... [to improve] Russian-American relations from their [current] crisis state".
Mr Putin also said he had confidence in "building a constructive dialogue between Moscow and Washington that is based on principles of equality, mutual respect and a real accounting of each other's positions, in the interests of our peoples and the world community".
Sergei Mironov, leader of the Fair Russia party, said: "As a man, I am not envious of Bill Clinton, because it seems he's a little wife who's followed Hillary Clinton to all the states like an old rucksack and now she's lost.
"This is the choice of Americans, as we always say. Russia will work with the president, elected by the American people."
Liberal Democrat boss Vladimir Zhirinovsky meanwhile said: "We will make up Mr Trump a telegram of congratulations: Dear Donald, we congratulate you on a well-deserved victory. Grandmother Hillary can take some rest now."
Mr Putin has tacitly supported the millionare property mogul during the campaign, while Mr Trump has repeatedly flattered and praised the Russian leader and said he was willing to work with him.
Father-of-five Mr Trump also denied ever meeting the Moscow leader, despite reports to the contraty.
Hungary's Prime Minister Viktor Orbán meanwhile said Mr Trump's victory is "great news" and shows "democracy is still alive."
Mr Orbán has been often criticised by the United States, including by Hillary Clinton when she was Secretary of State, for weakening the democratic system of checks and balances.
But Mr Orbán offered his congratulations to Trump on his Facebook page.