Joshua was elected as Mayor of Holyoke on November 2, 2021 after three and a half years as Town Administrator of Blandford, Massachusetts. Prior to that, Joshua worked at the Pioneer Valley Planning Commission and the Holyoke Housing Authority in various capacities. He has also served as a member of the Holyoke School Committee, Holyoke Fire Commission, Holyoke Community College Foundation, the Public Health Institute of Western Massachusetts, the MIIA Health Group Trust, and Nueva Esperanza in Holyoke.

Joshua is a lifelong resident of Holyoke, having gone through the public school system and Holyoke High School, before attending Westfield State University, where he earned both his bachelors and masters degrees. He lives with his wife, Stefany, and two children, Ethan and Allison.