Israel applied its administration and law to the Golan in 1981, but other governments did not recognise the act. Trump declared his break with that policy in a tweet.
Members of Netanyahu's ruling Likud party were quick to praise the prime minister for the shift in USA policy.
The Trump decision to recognize the Golan now gives Netanyahu a significant boost before the election, but will also also trigger criticism that the USA president is blatantly meddling in the Israeli elections.
Iran has faced economic hardship since U.S. President Donald Trump withdrew a year ago from the 2015 nuclear deal between Tehran and world powers and reimposed sanctions.
The announcement marks a diplomatic coup for Netanyahu, two weeks before elections, and four days before he is due to visit Washington.
"If some (thing) will happen from Lebanon toward Israel, we will hold Lebanon as the responsible (party)", Rivlin said.
"President Trump's decision to recognize the Golan as part of Israel is strategically wise and overall awesome".
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Trump called the Golan - a strategic area seized from Syria and annexed in a move never recognized by the global community - "of critical strategic and security importance to the State of Israel and Regional Stability!" Last week, the State Department dropped a reference to the Golan being under Israeli occupation.
President Trump wrote on Twitter that Israel should have full sovereignty over the Golan Heights, which Israel seized from Syria during the 1967 Six-Day War. Lindsey Graham, a staunch Trump ally, visited the Golan Heights with Netanyahu on Monday and pledged to promote Israel's sovereignty over the adea 'now and forever'.
During Pompeo's Jerusalem trip, there was also speculation that his Western Wall visit with Netanyahu could be interpreted as tacit approval of Israel's claim to sovereignty over the site.
"It's going to create real problems with our Arab partners in that part of the world", he said.
Trump's latest shakeup comes ahead of the expected unveiling of a White House plan for Israeli-Palestinian peace.
The secretary said he thought it was important to visit the wall with the Israeli leader as a show of support for Israel.
Netanyahu is scheduled to meet with Trump at the White House twice next week.
Trump's move appeared to be his most overt yet to help Netanyahu, who is locked in a closely contested race in the April 9 election while also fighting allegations of corruption, which he denies. In recent years, Israel has carried out many airstrikes in Syria to halt what it says are Iranian arms transfers to the Hezbollah militant group, and to prevent Iran from establishing a permanent military presence in the country.