The short answer is, maybe.
Article II, Clause 1:
[H]e shall have Power to grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment.
The only explicit limitation on the pardon power is that the president may not pardon himself or others from impeachment. In any case, impeachment is not a criminal prosecution, but rather an political effort to remove the president from his office.
Implicitly, the president may only pardon himself and others with respect to federal crimes: “Offenses against the United States.” The president still could conceivably be prosecuted for crimes that occurred in, say, New York by the State of New York. A separate pardon from the Governor of New York would be required to clear the president of wrong-doing in New York.
Nixon & the Pardon
Shortly before President Nixon resigned from office, the Office of Legal Counsel issued an opinion in which they cautioned that no one may be a judge in his own case. In effect, the OLC said, that the president cannot pardon himself.
Nixon was ultimately pardoned by his successor, Gerald Ford.