Giuliani, once considered a possible choice as Trump's secretary of state, had told the Republican of his decision during a meeting on Nov. 29, the team said in a statement.
CNN reported earlier on Friday, citing an unnamed source, that Giuliani had been told he was no longer in contention for the top U.S. diplomat post.
"Rudy Giuliani is an extraordinarily talented and patriotic American. I will always be appreciative of his 24/7 dedication to our campaign after I won the primaries and for his extremely wise counsel," Trump said in the statement. "He is and continues to be a close personal friend, and as appropriate, I will call upon him for advice and can see an important place for him in the administration at a later date.
"Rudy would have been an outstanding member of the Cabinet in several roles, but I fully respect and understand his reasons for remaining in the private sector," said Trump, who takes office on Jan. 20.
Reince Priebus, Trump's incoming White House chief of staff, said in the statement that Giuliani “was vetted by our team for any possible conflicts and passed with flying colors."
Other contenders include 2012 Republican presidential nominee and former Massachusetts Governor Mitt Romney and Exxon Mobil Corp Chief Executive Rex Tillerson.