The controversial leader spoke about the billionaire tycoon at a news conference in Qatar, making the comments to cheering supporters.
Mr Duterte, who has come under fire over his brutal war on drugs, likened himself to the Republican leader.
He said: “Trump is a realist, a pragmatic thinker.”
Making reference to Mr Trump’s staunch rejection of his critics, he continued: “You just think that, you know, both of us pretend that if we're insulted, we speak that way. But they don't know that in the case of Trump, he thinks deeply.”
He then praised the US President for his achievements in business.
Rodrigo Duterte praised Donald Trump and likened himself to the US leader
Trump is a deep man, he just pretends otherwise
Mr Duterte said: “Trump wouldn't become a billionaire if he were stupid.
“Have you seen his building? How can he be stupid? Trump is a deep man, he just pretends otherwise.
“Like me – I’m not really very bright.”
The remarks were met with resounding applause at the event.
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It comes after he previously endorsed positive relations with the United States with an impression of Mr Trump during a conversation between the pair.
Shocking images depict Philippines' war on drugs
Mon, March 20, 2017
Warning: Graphic content. Philippine President Rodrigo Duterte declared a war on crime and drugs after winning the presidential elections on May 9, 2016. Several thousands of people have been killed since his inauguration
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Inmates watch as drug suspects are processed inside a police station on October 12, 2016 in Manila, Philippines
Rodrigo Duterte hosted a packed out conference in Qatar
Mr Trump also reportedly praised Mr Duterte for his controversial campaign against drugs, in which thousands are thought to have died, during a phone call in which Mr Duterte congratulated him on his election victory.
In a statement, Mr Duterte said: “He [Mr Trump] was quite sensitive also to our worry about drugs. And he wishes me well… in my campaign and he said that we are doing it as a sovereign nation, the right way.”
A spokesman for Mr Trump's transition team said: "In their conversation, they noted the long history of friendship and cooperation between the two nations, and agreed that the two governments would continue to work together closely on matters of shared interest and concern."
The conversation followed a foul-mouthed attack on Barack Obama, who had criticised Mr Duterte’s policy on drugs.
Mr Duterte said: "Who does he think he is? I am no American puppet.
“I am the president of a sovereign country and I am not answerable to anyone except the Filipino people. Son of a w****, I will swear at you.”
Addressing the drugs problem at another press conference last year, the 72-year-old vowed to kill millions of drug users.
He said: “Hitler massacred three million Jews… there’s three million drug addicts. There are.
“I’d be happy to slaughter them.”