'completed a review' is correct and usable in written English.
You can use it when you are referring to reviewing something, such as a movie, book, or product. For example, "I recently completed a review of the latest John Grisham novel."
In 2011, the National Science Foundation completed a review and upheld Mann's work.
But the administration has not completed a review of Iran policy begun in 2001.
BrownCo completed a review for its account by naming McCann Erickson Worldwide in New York as agency of record.
A Wells notice advises that S.E.C. staff members have completed a review of the case and may recommend action by the full commission.
Jay has completed a review of the inquiry's work and, in an update this week, revealed that further public investigations may not take place.
Purdue University has completed a review of "tabletop fusion" experiments by one of its professors but is not saying what it found.
On March 27, the diocese completed a review of personnel files for about 500 priests dating back 50 years, and said that allegations were found against 13 priests.
On Sept. 9, General Miller completed a review of operations in Iraq and recommended a detainee interrogation policy that borrowed heavily from the procedures approved for Guantánamo.
On Long Island, the Diocese of Rockville Centre just completed a review of the files of more than 300 clergy members.
General Dynamics has extended the deadline for completing its proposed acquisition of Anteon International because the federal government has not completed a review of the $2.2 billion transaction.
Vick has remained on the Falcons' payroll, but N.F.L. Commissioner Roger Goodell barred him from training camp while the league completed a review of his case.
