President Barack Obama's party has secured crucial control of 60 seats in the US Senate, after the last undecided seat was awarded to a Democrat.
The Minnesota Supreme Court confirmed that Al Franken had narrowly won November's poll in the state.
On election night Republican Norm Coleman was given a small lead, prompting a recount won by Mr Franken but challenged by Mr Coleman.
Sixty of the 100 seats in the Senate can help defeat delaying tactics.
The Democrats need control of three-fifths of the Senate to overcome a Republican filibuster - a method used by minority parties to delay or prevent voting by excessive speaking.
Filibuster: From Dutch word "vrijbuiter" meaning "pirate". An attempt to block or delay Senate action on a bill or other matter by debating it at length, by offering numerous procedural motions, or by any other delaying or obstructive actions
Cloture: The only procedure by which the Senate can vote to place a time limit on consideration of a bill or other matter, and so overcome a filibuster. The Senate may limit consideration of a pending matter to 30 additional hours, but only by a vote of three-fifths of the full Senate, normally 60 votes
Source: US Senate
But although Mr Franken's win gives the Democrats the biggest Senate majority in 30 years, the party cannot always rely on unanimity in its ranks, says the BBC's Richard Lister in Washington.
Two of the votes Democrats rely on come from independents, while some Democratic senators will not automatically back the administration's agenda.
Even President Obama has acknowledged that he does not anticipate having what he called a "rubber-stamp Senate."
In addition, two prominent Democrats, Senator Ted Kennedy and Senator Robert Byrd, have missed a number of votes because of illness and cannot be relied on to be present in the chamber.
Mr Coleman, the Republican candidate, fought a protracted legal battle to overturn the results of the recount.
His legal team argued that a number of absentee ballots had been unfairly rejected by local officials.
The people of Minnesota will now finally get the brilliant and hardworking new senator they elected in November
Harry Reid Senate Majority Leader
But the Minnesota Supreme Court rejected Mr Coleman's arguments.
"The Supreme Court has made its decision and I will abide by the results," Mr Coleman told reporters.
Mr Franken hailed the result, saying he was "thrilled and honoured by the faith Minnesotans have placed in me".
Mr Franken first came to prominence as a comedian, appearing on Saturday Night Live.
He later became a best-selling author and a host on the liberal Air America radio station.
Democratic Senate Majority Leader Harry Reid issued a statement to "congratulate Senator-elect Al Franken, the next senator from the state of Minnesota".
He added: "The people of Minnesota will now finally get the brilliant and hardworking new senator they elected in November and the full representation they deserve."
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