The U.S. president "read early drafts of the bill and negotiated regarding critical elements of it," the White House said in a statement.
"He has now reviewed the final version and, based on its responsiveness to his negotiations, approves the bill and intends to sign it," it added.
The bill will also grant U.S. Congress the power to block Trump from unilaterally lifting sanctions on Russia.
This bill came although Trump administration officials had called on lawmakers to grant "flexibility" to the White House in dealing with Russia.
Trump's approval of the bill came after Russia announced that it would scale down U.S. diplomatic staff in Russia to 455 people and seize a U.S. warehouse and a recreational compound known as a "dacha" in Moscow in retaliation for Washington's anti-Russian actions.
Russia is forced to respond to U.S. sanctions while it is still willing to normalize bilateral relations, Russian Foreign Minister Sergei Lavrov told U.S. Secretary of State Rex Tillerson by phone on Friday.
These moves were caused by a series of hostile actions by Washington, including "unlawful" sanctions and "slanderous" accusations against Russia, said Lavrov, according to a statement of the Russian Foreign Ministry.