Before the vote, Ugandan Defence Minister Kiryowa Kiwanuka told MPs Trump had, through emissaries, contacted Uganda's President Yoweri Museveni in July seeking the country's contribution to the international force.
An Israeli official said last month people from "friendly countries" including Uganda could join the force if it was deployed.
Thursday's parliamentary debate was the first time Uganda itself had publicly acknowledged it might take part.
After a fragile ceasefire deal was struck in October, Trump set out a peace plan for the Gaza Strip that provided for a surge in humanitarian aid, civilian administration by Palestinian technocrats, Hamas laying down its arms and Israeli forces withdrawing.
The plan has stalled and the group of technocrats - known as the National Committee for the Administration of Gaza - has remained outside the enclave.
Under the plan, an International Stabilisation Force (ISF) is envisioned deploying in areas that are not under Israeli control.
It is unclear when any such force will deploy.
At the end of July, the Israeli security cabinet granted authorisation for part of the ISF, as well as representatives of the Palestinian Interim Administration, to begin work shortly in a limited area in Rafah in the south of the Gaza Strip.
Uganda is one of the largest contributors of troops to peacekeeping missions in Africa.
It has contingents deployed in several countries including Somalia, South Sudan and the Democratic Republic of Congo.
"Following the invitation by His Excellency Donald Trump ... the President of the Republic of Uganda, is ready to deploy in the Gaza Strip the desired Uganda People's Defence Forces contingent," Kiwanuka told MPs.
During the debate, some MPs asked about the legal arrangement that would govern the deployment.
Kiwanuka said a status of forces agreement would be signed after the vote.
Much of the Gaza Strip remains in ruins from two years of full-scale war triggered by the Hamas-led attacks on Israel on October 7, 2023.
with DPA
