The legislation bars Trump from easing or waiving the penalties on Russia unless Congress agrees.
In its statement, the White House said Trump "negotiated regarding critical elements" of early drafts of the bill and approved of the final draft "based on its responsiveness to his negotiations."
The Senate passed the bill, 98-2, two days after the House of Representatives pushed the measure through by an overwhelming margin, 419-3. Both were veto-proof numbers.
"He has now reviewed the final version and, based on its responsiveness to his negotiations, approves the bill and intends to sign it," Sander said without giving a time frame when it would be signed into law.
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The new sanctions come as the White House grapples with several ongoing probes into ties between the Trump campaign and Russia, which the President has blasted as unnecessary.
The legislation, could put strain on Trump's ability to improve ties with Russia, which he has vocally pursued, but has been restrained by the allegations that his associates had contacts with Russian officials during the election campaign.
Other than Russia, the legislation also seeks to make Iran pay for its "continued support of terrorism", and includes provisions to curb North Korea's nuclear programme.
Before President Barack Obama left office, he ordered the seizure of two Russian diplomatic compounds and expelled 35 of its diplomats in response to alleged election interference, a claim that Moscow has consistently denied.
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