Harrison defeated Wilson by a count of 466 to 341, according to official vote totals.
"Winning this election would not have been possible without the hard work of my campaign committee and many others," Harrison said in a statement. "I would like to extend best wishes to Patrick Wilson who has made valuable contributions to the town. I look forward to working with my fellow selectmen to actively engage in helping to move the town of Wenham forward."
William Dery, Roger Kuebel, Stacey Metternick, and Lawrence Swartz were all elected to the School Committee.
The race was the only contested one on Thursday's ballot.
The voter turnout was 30 percent. Of the 2,749 registered voters in town, 824 cast a ballot Thursday.