But if Democrats had blocked Wright, Republicans could have retaliated and derailed other nominations.
Wright will have to recuse himself from the most significant case currently before the FTC: its antitrust investigation of Google.
Wright, who received funding from Google for some of his academic research, pledged not to participate in any FTC actions involving the company for two years.
Clyburn, the daughter of Rep. James Clyburn (D-S.C.), is a vocal advocate for media diversity, and pushed the commission to look into the high rates that prisoners pay for phone calls to their families.
In a statement, FCC Chairman Julius Genachowski said he looks forward to continuing to work with her.
"Commissioner Clyburn is an excellent and dedicated public servant and has been a strong advocate in seeking to extend the benefits of broadband to all Americans," he said.
On Sunday, the Senate confirmed William Baer to head the Justice Department's Antitrust Division in a 64-26 vote. The division has not had a permanent chief since August 2011, when Christine Varney left for private practice.