Clough, who returned for a second spell in charge in December, first managed Burton in the sixth tier in 1998.
He led the club to the brink of the Football League in 2009 and they have now secured back-to-back promotions.
"When we came 17 and a half years ago we had a five-month old baby. He is 18 today," Clough told BBC Radio Derby.
Burton drew 0-0 at Doncaster on Sunday to finish second in League One and clinch automatic promotion to the second tier for the first time in the club's history.
Clough added: "It's an emotional time for everybody to get to this point, 17 and a half years on from where we started, it is truly, truly remarkable.
"It's my son's 18th - we're going to have one of the biggest parties Burton's seen.
"To come from where we've come from in that time I think is incredible in football terms."
Clough, son of legendary Nottingham Forest boss Brian, will lead Burton into the second tier next season, where they will face Forest and another former European Cup winner, Aston Villa.
Manager Nigel Clough said celebrations after Burton's rise to the Championship were made extra special as his son's 18th birthday fell on the same day.