Kraft previously worked for twelve years as CEO of the Boys & Girls Club's Boston chapter.

In a 2008 profile, Mary Moore of Boston Business Journal idiomatically described his upbringing as having included "silver-spoon comforts" by virtue of his family wealth.

Kraft is considered a well-recognized figure in the city of Boston, both due to his work at nonprofits and his status as a scion of a wealthy and high-profile family.

[4] In a 2008 profile written after Kraft was elevated to an executive position at Boys & Girls Club of Boston, Mary Moore of Boston Business Journal idiomatically described Kraft as having "traded silver-spoon comforts for passion and street savvy" in his work with this branch of the Boys & Girls Club, and as having "earned him both popularity and respect" from members of the branch.

She also described him as, "the rare nonprofit leader whose raw enthusiasm for the organization’s mission comes from so many years spent at its grassroots level.

"[4] Kraft became president and chief operating officer (CEO) of the Boys & Girls Club of Boston in July 2008,[4][1][9] a role he held for twelve years.

[11] Kraft partnered the organization with the Massachusetts Military Support Foundation to provide meals to veterans and their families.

[7] During the governorships of Charlie Baker and Maura Healey, Kraft was co-chair of the governor's task force on hate crimes.

[13] At the federal level, Kraft has given sizable personal donations to House and Senate candidates from both the Democratic and Republican parties.

[14] During the 2023 Boston City Council election, Kraft donated to a slate of candidates that had been prominently backed by New Balance CEO, major Republican donor,[15] and Trump supporter[16] Jim Davis.

[7] There was also speculation that Kraft might challenge incumbent U.S. congresswoman Ayanna Pressley in the 2024 Democratic primary for Massachusetts's 7th congressional district.

During his speech where he announced his candidacy, he heavily criticized Michelle Wu, saying that she had not fulfilled campaign promises to make the MBTA free for residents of Boston, enact rent control and implement the Green New Deal in the Boston Public Schools system.

[27] The Boys & Girls Club of Boston has named one of its facilities the "Josh Kraft Mattapan Teen Center".