The Trotters took the lead after Ruben Rodrigues capitalised on a mistake from goalkeeper Corey Addai to score after two minutes.
Stockport thought they had responded quickly but their equaliser was ruled out following a VAR review for a foul in the build-up.
Adama Sidibeh eventually levelled for the Hatters before half-time with a clever header, but it was Bolton that regained control after the break when Kyle Wootton turned the ball into his own net.
Sam Dalby’s spectacular scissor-kick extended the lead before Rodrigues added a late penalty in stoppage time.
The victory ends Bolton’s lengthy exile from the Championship following their relegation in 2019, while Stockport missed out on a return to the second tier for the first time in 24 years.