ACT is more than 40 years old.
The personal insight that led to ACT is described by Steve Hayes in this TEDx talk: bit.ly/StevesFirstTED. By his best memory, that moment on the carpet (you will understand that phrase if you see the talk) was in the winter of 1980-81. But that was just a transformational moment. ACT began to form in Steve's lab soon after. The lab members at the time included Robert Zettle ("the Z"), Zamir Korn, and Irwin Rosenfarb. The lab was jointly run with the late Aaron Brownstein, a basic behavior analyst.
The first ACT protocol was written by Steve in 1981. ACT was called "Comprehensive Distancing" -- the lab nickname for it was "Big D." You can find the protocol in the "History of ACT" daughter page of the "About ACT" section of the website.
The first actual ACT study was done in 1981-1982 and was presented at ABCT (then called AABT) in 1982:
Hayes, S. C., Korn, Z., Zettle, R. D., Rosenfarb, I., & Cooper, L. (November 1982). Rule‑governed behavior and cognitive behavior therapy: The effects of comprehensive cognitive distancing on pain tolerance. Paper presented at the meeting of the Association for Advancement of Behavior Therapy, Los Angeles.
Steve held back on publishing it despite its success, thinking that the implications were too large and thus outcome studies should not be a focus (especially randomized outcome studies) until its model and methods were better understood and idiographically tested. That is why this very first study was published 17 years later: Hayes, S. C., Bissett, R., Korn, Z., Zettle, R. D., Rosenfarb, I., Cooper, L., & Grundt, A. (1999). The impact of acceptance versus control rationales on pain tolerance. The Psychological Record, 49, 33-47. The only randomized outcome study published directly from the lab in this era was Rob Zettle's dissertation which came out in 1986.
The first ACT training was in 1982: Hayes, S. C. (October 1982). Cognitive distancing and psychopathology. Presentation to Broughton Hospital, Morganton, NC.
"Comprehensive distancing" seamlessly morphed into ACT as we think of it today. The first time "acceptance and commitment therapy" was used in the title of a talk was in 1991: Wilson, K. G., Khorakiwala, D., & Hayes, S. C. (May 1991). Change in Acceptance and Commitment Therapy. Paper presented at the meeting of the Association for Behavior Analysis, Atlanta. The first time it appeared in the title of a journal article was Hayes, S. C. & Wilson, K.G. (1994). Acceptance and Commitment Therapy: Altering the verbal support for experiential avoidance. The Behavior Analyst, 17, 289-303.