Mr Trump called it an "honour and privilege" to nominate Judge Kavanaugh, who became a judge for the US Court of Appeals in 2006, and said he had "impeccable credentials and unsurpassed qualifications".
"In keeping with President Reagan's legacy, I do not ask about a nominee's personal opinions. What matters is not a judge's political views, but whether they can set aside those views to do what the law and the constitution require," Mr Trump said.
"Judge Kavanaugh has impeccable credentials and a proven commitment to equal justice under the law — he is considered a judge's judge, a true thought leader among his peers.
"He is a brilliant jurist, with a clear and effective writing style, universally regarded as one of the finest and sharpest legal minds of our time."
The vacancy on the nation's highest court was caused by the retirement of Justice Anthony Kennedy.
In picking the 53-year-old Kavanaugh, Mr Trump aimed to entrench conservative control of the court for years to come with his second lifetime appointment to the nation's highest judicial body in his first 18 months as President.