He urged the winners to withdraw from their parties and "govern as independents in name and in spirit."
"It is probably the biggest contribution you can make to the country," he wrote.
Brin has not been as politically active as Google Chairman Eric Schmidt, a vocal supporter of President Obama, but he did donate to the president's reelection campaign.
According to campaign finance records, in October 2011, Brin donated the maximum $5,000 to Obama's campaign and $30,800 to the Democratic National Committee.
In September, Brin attended a bill signing with California Gov. Jerry Brown (D) at Google's headquarters in Mountain View. The law will allow Google and other companies to operate driver-less cars on public roads.