The Senate voted 94-6 to approve Rosenstein as the number two man at The Department of Justice.
As the second-in-command under Attorney General Jeff Sessions, Rosenstein's confirmation hearing was mostly centered on Sessions' own undisclosed discussions with the Russian ambassador to the U.S., Sergey Kislyak, and eventual recusal from Justice Department investigations regarding Russia.
But Blumenthal said Rosenstein's failure to commit to appointing a special prosecutor to investigate ties between the Trump administration and Russian Federation forced him to vote against the nomination.
A Justice Department spokesman did not respond to a question about when Rosenstein will be sworn in.
A person named as special counsel "shall be a lawyer with a reputation for integrity and impartial decisionmaking, and with appropriate experience to ensure both that the investigation will be conducted ably, expeditiously and thoroughly, and that investigative and prosecutorial decisions will be supported by an informed understanding of the criminal law and Department of Justice policies", the regulation states.
Rosenstein served as Maryland's attorney general for almost 12 years.
Rosenstein, 52, was appointed to serve as USA attorney for Maryland in 2005 by then-President George W. Bush and was kept in the job by President Barack Obama. Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa) said last month he would hold up the vote on Rosenstein until FBI Director James B. Comey briefed his panel about probes into alleged ties between the Trump administration and Russian officials - a matter that was then out of Rosenstein's control.
"How I would handle an investigation.is how I would handle any investigation", Rosenstein said.
Rosenstein will be in charge of overseeing the investigation into Russia's meddling in the 2016 presidential election, including potential connections between Trump campaign officials and Moscow.