Evesham Township, New Jersey. Evesham Township is a township in Burlington County in the US state of New Jersey, United States. As of the 2010 United States Census, the township's population was 45,538, reflecting an increase of 3,263 (+7.7%) from the 42,275 counted in the 2000 Census, which had in turn increased by 6,966 (+19.7%) from the 35,309 counted in the 1990 Census.