Paulinho's first-half goal at the Stadio Armando Picchi was enough to settle a 1-0 victory and complete a 2-1 aggregate win over Empoli in the two-legged Serie B play-off final, restoring Livorno to the top flight after three years away.
But the Tuscan club are still grieving the death of Morosini, who suffered a fatal cardiac arrest during a league match at Pescara in April 2012, and Spinelli paid tribute to the 25-year-old midfielder.
He told La Repubblica: "I dedicate this promotion to Morosini.
"I said that I would get Livorno back into Serie A in three years and my word counts for a lot. We had the best season I've seen through my time here, we were second or third throughout.
"We then tackled the lottery of the play-offs where one wrong move can ruin your campaign, but Morosini gave us a hand from up on high."
Spinelli also gave his backing to 40-year-old head coach Davide Nicola, who earned Livorno promotion at the end of only his first campaign on the west coast.
"He has the same kind of support I gave to (Roberto) Donadoni and (Walter) Mazzarri," Spinelli added. "I'm committed to his cause and we've already given him a two-year contract extension.
"Nicola has earned the chance to coach in this league and in a couple of years' time he could go on to manage a big club."