America is Northern Ireland's number one overseas investor, with its firms employing about 23,000 people in NI.
Mr Hamilton said he is "not concerned at all" about future US investment and jobs.
During his campaign, Mr Trump pledged protectionist trade arrangements and to cut the US corporation tax rate.
Northern Ireland is reducing its rate to 12.5% from 2018 to attract more overseas companies, including from America.
"I think the US will continue to be a great, close friend," Mr Hamilton said.
"They have been a great supporter of our economic progress down the years and I am absolutely sure Mr Trump will want to continue that."
Northern Ireland Secretary James Brokenshire also believed the outlook was "positive."
He said: "When I was in Washington in September a number of US companies underlined their continued commitment to Northern Ireland.
"We want to see that flourish and grow."
There are 185 US firms in Northern Ireland.
Northern Ireland exports Â£1.5bn worth of goods to America a year, according to figures from HM Revenue and Customs.
Economy Minister Simon Hamilton has said Northern Ireland is "looking forward" to working with incoming US President Donald Trump.