Israel captured the Golan from Syria in a 1967 war and annexed it, in a move not recognized internationally. The United States broke with other world powers last month when Trump signed a decree recognizing Israeli sovereignty there.
"All Israelis were deeply moved when President Trump made his historic decision," Israeli Prime Minister Benjamin Netanyahu said in a video statement made on the Golan.
He added that, after the Jewish Passover festival, he would "bring to the government a resolution calling for a new community on the Golan Heights named after President Donald J. Trump."
Trump's Golan move followed his decision in December 2017 to recognize Jerusalem as the Israeli capital, breaking with decades of U.S. policy over the status of a city contested by the Palestinians.
The decision came only two weeks ahead of a tightly contested Israeli election, which saw Netanyahu win a fifth term in office.
Israel has said separately that, in appreciation of the U.S. president, it intends to name a proposed train station near Jerusalem's Western Wall after him.
Around 18,000 Syrians from the Druze sect — most of whom refuse to take Israeli citizenship — remain in the occupied Golan.
Some 20,000 Israeli settlers have moved there, spread over 33 settlements.