The President has no legal authority to declare himself winner.
State election officials -- not the President or any other federal official -- certifies state election results. The U.S. Congress follows suit.
Each state faces a deadline, set by its own legislature, by which its officials must finish tallying votes and certifying the results. After the results are certified, states present a slate of "electors", individuals representing the state at the Electoral College.
According to the U.S. Code, states should finish tallying their results and resolve any court contests by December 8, or risk Congress rejecting their nominated electoral college representatives. One week later, on December 14, the states' Electoral College members meet to formally cast their votes.
On January 6, the newly-sworn in Congress affirms the results and hands them to the Vice President, who pronounces them official. The President of the United States has no role in this process, and no legal authority to declare the winner of any state election.
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