Town will head to Stamford Bridge to face the European champions and eight-times FA Cup winners in the third round in early January.
Rowe watched the draw at home with his partner and young son Arthur.
Describing his reaction when ball number 13 was drawn at home to 61 by former England goalkeeper David Seaman, Rowe told the DT: "I leapt for joy and there was a big noise that came out so it scared him, bless him!
"It was a fantastic feeling. I am sure it was the same amongst all of the supporters and everyone connected with the club.
"I always trusted Seaman when I was growing up – a safe pair of hands – so it was quite ironic that he pulled us out!
"It is great for the club. When the club was down on its knees the community trust stuck their neck out and this is the reward that they get.
"The trust and the players deserve it. They have worked so hard on and off the field. You make your own luck sometimes in life and they certainly have earnt that so it is credit to everybody.”
The meeting between the two clubs will be the first in more than 70 years since they clashed in the FA Cup in 1950, with Chelsea winning a replay 3-0 after a 1-1 draw at Saltergate.
Chesterfield were actually the first-ever team to win at Stamford Bridge in a league game in 1905.
The Spireites, who have beaten Curzon Ashton, Southend United and Salford City to reach this stage of the competition, are set to make a six-figure sum from the match.
Rowe, who has recently just marked his first year in charge of the Blues, said drawing the four-times Premier League winners was an ‘immensely proud day.’
“It is bigger than me, it is not about me, it is about the club,” he explained.
"Personally, of course I would love to go up against their manager but it is a pat on the back for the community trust and the players’ hard work.
"The challenge now is to stay focused on the league and we can get excited about Chelsea in January.
"It is in the bag for us, it is a lovely early Christmas present for everybody and something we can really look forward to as a club, but we can only look forward to it really in January in terms of on the pitch. I am sure the supporters can be excited for the next three weeks.
"I don’t know what the allocation will be but I am sure we are going to fill it and some.
"It is incredible to think where we were just a year ago, second from bottom, to where we are in the league now, and then to draw them out of the hat was a great day.”
As a Spurs fan, Rowe will no doubt relish the opportunity to face rivals Chelsea.
And what a moment it will be for him when he faces German Thomas Tuchel, who has won 11 trophies in his managerial career, including the Champions League with Chelsea last season. At PSG he won two league titles, the French Cup and the French League Cup and the German Cup with Borussia Dortmund.
Tuchel is the first German to manage Chelsea, signing a two-and-a-half-year contract last January after replacing Frank Lampard.
"There is a bit of rivalry (between Chelsea and Spurs) there but as a manager you look at games with different eyes,” Rowe said.
"It is a dream come true where I am in my career personally and what I can learn from that day.
"We respect them so much and he (Tuchel) is a coach that I admire. He has come in and made a real difference to that Chelsea team and obviously losing the FA Cup last season will mean they will want to go the whole way this year I am sure but they have got bigger priorities like the Champions League and the league title.
"For us, our objective at the start of the year was to try to get back into the EFL and anything else is a bonus for the club and this is a big bonus for us. It is a bonus game.
"I am sure when the occasion comes it will be a great occasion for us and for me personally to go up against Thomas.”
But for now Chesterfield’s focus will be on maintaining their position at the top of the National League and they face a trip to promotion rivals Grimsby Town this Saturday.
The Mariners, who were relegated from League Two last season, are sixth in the table and are four points behind the Spireites although they have played one more game.
The two sides met in pre-season, with Chesterfield winning 2-1 at the Technique Stadium.
"We have got to keep grounded, we can’t let it be a distraction,” Rowe added.
"You work hard every day, especially at these levels, and sometimes you don’t get your rewards as much as the players higher up in the pyramid so the players fully deserve this.
"I trust them to be professional in what they are doing.
“Grimsby is the next one on our radar and nothing changes. We have been out this morning working.”