Israel and the Palestinian militant group Hamas agreed last month to the first phase of Trump's 20-point plan for Gaza - a ceasefire in their two-year war and a hostage-release deal - but the UN resolution is seen as vital to legitimising a transitional governance body and reassuring countries that are considering sending troops to Gaza.
The text of the resolution says member states can take part in the Trump-led Board of Peace envisioned as a transitional authority that would oversee reconstruction and economic recovery of Gaza.
It also authorises the international stabilisation force, which would ensure a process of demilitarising Gaza, including by decommissioning weapons and destroying military infrastructure.
Hamas reiterated it won't disarm and argued that its fight against Israel is legitimate resistance, potentially pitting the militant group against the international force authorised by the resolution.
"The resolution imposes an international guardianship mechanism on the Gaza Strip, which our people and their factions reject," Hamas said in its statement, issued after the adoption of the resolution.
UN Secretary-General Antonio Guterres hailed the agreement as an opportunity to "transform the ceasefire into a lasting peace".
US ambassador to the UN Mike Waltz said the resolution, which includes Trump's 20-point plan as an annex, "charts a possible pathway for Palestinian self-determination ... where rockets will give way to olive branches and there is a chance to agree on a political horizon".
"It dismantles Hamas' grip, it ensures Gaza rises free from terror's shadow, prosperous and secure," Waltz told the council ahead of the vote.
Trump celebrated the vote as "a moment of true Historic proportion" in a social media post.
"The members of the Board, and many more exciting announcements, will be made in the coming weeks," Trump wrote.
Russia, which holds a veto on the Security Council, earlier signalled potential opposition to the resolution but abstained from the vote, allowing the resolution to pass. China also abstained.
The UN ambassadors of Russia and China, which also abstained, complained that the resolution does not give the UN a clear role in the future of Gaza.
"In essence, the council is giving its blessing to a US initiative on the basis of Washington's promises, giving complete control over the Gaza Strip to the Board of Peace and the ISF (international stabilisation force), the modalities of which we know nothing about so far," Russian ambassador Vasily Nebenzya told the council following the vote.
The Palestinian Authority issued a statement welcoming the resolution, and said it is ready to take part in its implementation. Diplomats said the authority's endorsement of the resolution last week was key to preventing a Russian veto.
The resolution has proven controversial in Israel because it references a future possibility of statehood for the Palestinians.
The resolution's text says that "conditions may finally be in place for a credible pathway to Palestinian self-determination and statehood" once the Palestinian Authority has carried out a reform program and Gaza's redevelopment has advanced.
"The United States will establish a dialogue between Israel and the Palestinians to agree on a political horizon for peaceful and prosperous coexistence," it says.
Prime Minister Benjamin Netanyahu, under pressure from right-wing members of his government, said on Sunday that Israel remained opposed to a Palestinian state and pledged to demilitarise Gaza "the easy way or the hard way".
