Speaking at a news conference in Washington, he denied any collusion with Russia during his election campaign last year.
"The entire thing has been a witch hunt and there is no collusion," he said.
Former FBI chief Robert Mueller has been selected to lead the inquiry.
Mr Mueller's appointment was welcomed by politicians from both sides.
Calls for a special investigation had mounted after Mr Trump fired FBI Director James Comey last week.
On Thursday, Mr Trump denied trying to influence the investigation by sacking Mr Comey.
"Director Comey was very unpopular with most people," he suggested.
"I actually thought when I made that decision... that it would be a bipartisan decision because you look at all of the people on the Democratic side, not only the Republican side, that were saying such terrible things about Director Comey."
On Wednesday, Mr Trump had said no politician in history "has been treated worse or more unfairly" than himself.
Robert Mueller (L) with his successor at the FBI James Comey, whose dismissal prompted calls for a wider investigation
The announcement of a special counsel apparently took the White House by surprise, with Mr Trump only being informed of it after Deputy Attorney General Rod Rosenstein had signed the order.
The FBI and Congress are looking into potential links between Mr Trump's campaign team and Russia. Mr Mueller will take over the FBI investigation.
US intelligence agencies believe Moscow tried to tip November's presidential election in favour of Mr Trump.
Meanwhile, the New York Times reports that former Trump aide Michael Flynn told his transition team at the beginning of January - earlier than was previously thought - that he was under federal investigation for working as a paid lobbyist for Turkey during the election campaign.
Mr Trump appointed Mr Flynn as his national security adviser weeks later despite the warning, but he was sacked after just 24 days.
Mr Flynn was sacked for misleading the vice-president about his contacts with Russian officials
In his statement announcing Mr Mueller's appointment, Mr Rosenstein said: "The public interest requires me to place this investigation under the authority of a person who exercises a degree of independence from the normal chain of command."
Mr Mueller, who will have wide-ranging powers, said simply: "I accept this responsibility and will discharge it to the best of my ability."