US international borders can be changed by treaty — negotiated by the State Department, signed by the President, final approval by the Senate. This has actually happened, in 1977 the US and Mexico swapped some islands in the Rio Grande.
In the US the county and state level seem to have no authority to action their own change of status, besides lobbying their representatives in Washington. It’s pretty clearly a federal power.
Canada’s a little different, as while the Commons is consulted on treaties, there’s no veto and treaties are approved by Order in Council. But it gets weird. A Canadian government could almost certainly accept new land as a Territory (or part of an existing Territory, if the Yukon/Alaska boundary were to shift), but accepting either an additional province or adding land to an existing province might cross constitutional authority lines. The government of Canada pretty clearly has the authority to accept Point Roberts from the US, but might not be able to grant it to BC without the approval of the BC provincial government.