The French forward fired the Royals into the Wembley final on Monday, 29 May for a shot at promotion to the Premier League just after half-time.
The only goal of the second leg came after Fulham centre-back Tomas Kalas was penalised for handball.
Fulham were denied a leveller by a string of excellent saves from Ali Al Habsi in the Reading goal.
The Royals, who finished third in manager Jaap Stam's first season in charge, will play either Huddersfield or Sheffield Wednesday in the final.
Shortly after full-time, Reading also announced that Chinese brother and sister Dai Yongge and Dai Xiu Li had become the majority shareholders of the club.
The two sides were level at 1-1 from Saturday's first leg at Craven Cottage and an opening half an hour of great intensity saw both goalkeepers make fine saves to keep the scores tied.
Goalscorer Kermorgant was denied an earlier opener by Marcus Bettinelli's fine right-hand stop after his low shot on the turn, before Al Habsi denied Fulham's Tom Cairney at the other end.
After the break, it was a lapse in concentration from Fulham centre-back Kalas that was to prove the decisive moment.
Kermorgant chased a ball over the top into the Fulham area and put pressure on Kalas, who was penalised by referee Martin Atkinson as the ball rolled up his left arm.
The 35-year-old striker converted the spot kick low to Bettinelli's right for his 19th goal of the Championship campaign.
Reading's progression to the final against a free-flowing and attacking Fulham owed much to their player of the season Al Habsi.
The Oman international, 35, was imperious throughout and kept his side in the game in the first half with a fine double save, first from Cairney's curling free-kick and then Sone Aluko's rebound.
Those quick reflexes came after he parried a Ryan Fredericks shot on to the base of the post.
In the second half, and with his side leading, he then tipped over a Kevin McDonald strike after Aluko had cut Reading open with some sublime skill down the right wing.
He still had time to deny substitute Chris Martin what looked like a simple finish as he dived to smother the ball at the striker's feet on the edge of the six-yard box.
Reading return to Wembley in a Championship play-off final for the first time since 2011, when they were beaten 4-2 by Swansea.
Fulham are yet to progress beyond the semi-finals of the format in the second flight.
Reading manager Jaap Stam:
"It was a tough game. We knew it would be from the start.
"In the first half we played well in how we got in behind and threatened, we tried to manage the space well and in the first half, we played very well and we were aggressive in how we pressed them.
"We spoke at half-time about how we could make it more difficult for them. We got a great start after the break, but then it was about us keeping on pressing them.
"We fought with everything we had. We've done that so many times this season and if you hold on like that, you will force mistakes out of people.
On reaching a Wembley final: "We worked so hard to get there. It's not all about football, sometimes it's all about results.
"We're proud in the achievement that we've done. It's great to be there to play in the final, I've been there in my playing career.
"There's a lot at stake and a great prize potentially for the club. It'll be tough against either Huddersfield or Sheffield Wednesday.
"It could be a game of great nerves, a great occasion, but we'll have to manage it properly."
On Ali Al Habsi's performance: "We know he's a great keeper, it's not just about today, he's been superb all season.
"It was a terrific performance. That's why he's paid to be in goal and be our last line of defence."
Fulham manager Slavisa Jokanovic:
"I believe we played the better football, we were the better team, but we're not off to the final.
"Reading scored two goals in this tie after complicated decisions. "These situations exist and the push in the box on Lucas Piazon for us didn't get the same treatment as his decision earlier at the opposite end of the pitch.
"But, Martin Atkinson is the best English referee, an international referee and I can't complain.
"We're really disappointed as we've lost the chance to play in the final after these kind of decisions.
"We weren't clinical enough tonight. On one side I'm disappointed but on the other, I'm proud of my team and how they play throughout the season."
Match ends, Reading 1, Fulham 0.
Second Half ends, Reading 1, Fulham 0.
Attempt missed. Chris Martin (Fulham) header from the centre of the box misses to the right. Assisted by Stefan Johansen with a cross following a corner.
Corner,  Fulham. Conceded by Garath McCleary.
Corner,  Fulham. Conceded by Joey van den Berg.
Substitution, Reading. Joseph Mendes replaces Yann Kermorgant.
Attempt missed. Tom Cairney (Fulham) header from the right side of the box misses to the right. Assisted by Lucas Piazon with a cross following a corner.
Corner,  Fulham. Conceded by Garath McCleary.
Corner,  Fulham. Conceded by Garath McCleary.
Foul by Ryan Fredericks (Fulham).
George Evans (Reading) wins a free kick in the attacking half.
Delay over. They are ready to continue.
Delay in match Ali Al Habsi (Reading) because of an injury.
Foul by Chris Martin (Fulham).
Ali Al Habsi (Reading) wins a free kick in the defensive half.
Attempt missed. Chris Martin (Fulham) right footed shot from very close range misses to the left. Assisted by Sone Aluko with a cross.
Corner,  Fulham. Conceded by Ali Al Habsi.
Attempt saved. Kevin McDonald (Fulham) right footed shot from the right side of the box is saved in the top centre of the goal. Assisted by Sone Aluko.
Substitution, Reading. Liam Kelly replaces John Swift.
Attempt blocked. Ryan Sessegnon (Fulham) left footed shot from outside the box is blocked.
Corner,  Fulham. Conceded by John Swift.
Sone Aluko (Fulham) wins a free kick on the right wing.
Foul by Joey van den Berg (Reading).
Substitution, Fulham. Chris Martin replaces Scott Malone.
Attempt missed. Sone Aluko (Fulham) left footed shot from the right side of the box is just a bit too high. Assisted by Stefan Johansen.
Attempt blocked. Tom Cairney (Fulham) left footed shot from outside the box is blocked. Assisted by Lucas Piazon.
Corner,  Fulham. Conceded by Garath McCleary.
Attempt missed. Yann Kermorgant (Reading) right footed shot from the centre of the box is high and wide to the right following a fast break.
Attempt saved. Ryan Sessegnon (Fulham) left footed shot from the left side of the box is saved in the bottom right corner. Assisted by Sone Aluko.
Substitution, Reading. Garath McCleary replaces Tyler Blackett.
Scott Malone (Fulham) is shown the yellow card.
Foul by Ryan Sessegnon (Fulham).
Chris Gunter (Reading) wins a free kick in the defensive half.
Offside, Fulham. Stefan Johansen tries a through ball, but Sone Aluko is caught offside.
Attempt missed. Stefan Johansen (Fulham) left footed shot from outside the box misses to the right. Assisted by Tom Cairney.
Corner,  Fulham. Conceded by Tiago Ilori.
Attempt blocked. Lucas Piazon (Fulham) left footed shot from the centre of the box is blocked. Assisted by Ryan Fredericks.
Corner,  Fulham. Conceded by Liam Moore.
Stefan Johansen (Fulham) wins a free kick in the attacking half.
Foul by Joey van den Berg (Reading).
A Yann Kermorgant penalty was enough for Reading to edge out Fulham and reach the Championship play-off final.