If signed into law, the bill would provide $1 billion in loan guarantees to Ukraine and further sanction Russia for its annexation of Crimea.
"We must target those guilty of aggression against Ukraine and stand by our allies and friends to ensure peace and security in Europe," said Rep. Ed Royce, R-Calif., the chairman of the House Foreign Affairs Committee.
Obama was wrapping up a three-country European trip during which he solicited support of allies in challenging Russia's moves in Ukraine. The rare congressional unity contrasted with recent partisan divisions over the Ukraine package, including disputes over new IRS regulations on groups claiming tax-exempt status and International Monetary Fund reforms.
In a retreat two days earlier, Senate Democrats backed down and stripped the IMF reform language from the bill, a defeat for the Obama administration, which had promoted the IMF provisions.
Ukraine, a nation of 46 million people, is battling to install a semblance of normalcy since Ukraine's pro-Russian president, Viktor Yanukovych, was ousted in February after months of protests ignited by his decision to back away from closer relations with the European Union and turn toward Russia.
On Thursday, the IMF pledged up to $18 billion in loans to prop up Ukraine's teetering economy. The money was hinged on structural reforms that Ukraine has pledged to undertake.
Other donors, including the European Union and Japan, already have pledged further aid to Ukraine, conditioned on the conclusion of an IMF bailout and reform package. The total amount of international assistance will be about $27 billion over the next two years.
Associated Press writer Donna Cassata contributed to this report.