With final votes still being counted, Republican challenger Dino Rossi said he had called Ms Murray to "offer my congratulations".
The result leaves the Democrats with 51 seats in the 100-member Senate following Tuesday's mid-term polls.
Republicans have 46 seats and two independents caucus with the Democrats. The Alaska vote is yet to be called.
The mid-term elections resulted in heavy losses for the Democrats.
The president's party lost control of the House of Representatives and despite the Washington state victory, has a reduced majority in the Senate.
US President Barack Obama campaigned for Ms Murray twice during the run-up to the polls, including at a rally in Seattle which took place just as voters were receiving their ballots.
Washington state has a large number of postal ballots, so counting the vote takes longer than in other parts of the country.
The Republican concession came as Ms Murray's lead hit about 46,000 votes out of more than 1.8 million counted - about three-quarters of the expected total cast.
Source:http://www.bbc.co.uk/news/world-us-canada-11700077
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