Leading 3-1 from the quarter-final first leg, Unai Emery’s team swatted aside Bologna with a 4-0 victory at Villa Park.
Forest, 12 spots below fourth-placed Villa in the Premier League, defeated 10-man Porto 1-0 in Nottingham to secure a 2-1 aggregate success.
Villa are into their second European semi-final under Emery after making the last four in the Conference League in 2024.
Europa League specialist Emery has won the tournament four times – three with Sevilla and one at Villarreal – and also finished as a runner-up with Arsenal.
Ollie Watkins had scored twice in the first leg in Italy and the England striker tormented Bologna again in the 16th minute.
It was an eye-catching goal as Villa’s flowing 14-pass move climaxed with Morgan Rogers setting up Watkins for a tap-in from six yards.
Watkins’ 100th goal for Villa made him the club’s top scorer in European competitions with 10, overtaking Peter Withe and John McGinn.
Villa missed a 25th minute penalty after Martin Vitik handled a header from Rogers, whose spot-kick was saved by Federico Ravaglia.
But it was only a temporary reprieve for Bologna as Emiliano Buendia struck with a fierce blast in the 26th minute.
Rogers made up for his penalty miss in the 39th minute, netting for the first time in 12 games with a drive that beat Ravaglia at his near post.
Ezri Konsa’s 89th-minute volley capped Villa’s dominant display.
At the City Ground, two-time European champions Forest booked their first continental semi-final since the 1983-84 Uefa Cup.
Porto defender Jan Bednarek was dismissed in the eighth minute for an ugly foul that caught Chris Wood on the knee and forced the New Zealand striker to limp off injured.
Emotion at Forest
Forest quickly took advantage of their numerical superiority as Morgan Gibbs-White’s shot from the edge of the penalty area took a hefty deflection before looping into the back of the net in the 12th minute.
Gibbs-White celebrated by holding up a shirt with Elliot Anderson’s name on it in a tribute to the Forest star, who missed the game due to the death of his mother.
There was another emotional moment at half-time when former Forest striker Tony Woodcock was presented with a winners’ medal from the 1980 European Cup.
Woodcock’s strained relationship with then Forest boss Brian Clough led him to be denied a medal after he left the club during their run to win the competition for a second successive season.
Forest had a narrow escape when Porto’s William Gomes hit the woodwork from close-range in the second-half and they rode their luck again in the closing minutes as Alan Varela struck the crossbar.
Playing in Europe for the first time since the 1995-96 Uefa Cup, Vitor Pereira’s side will hope their Europa run provides a boost in their battle to avoid relegation.
Freiburg swept into the Europa League semi-finals for the first time with a 3-1 win against Celta Vigo.
Julian Schuster’s side already had one foot in their first ever European semi-final after a 3-0 victory in the first leg in Germany last week.
They finished the job in Vigo, winning 6-1 on aggregate thanks to Igor Matanovic’s opener and Yuito Suzuki’s double.
Williot Swedberg’s stoppage-time strike was no consolation for out-classed Celta.
In the semi-finals, Freiburg will play Sporting Braga, who came from behind to win 4-2 at Real Betis, sealing a 5-3 aggregate triumph.
Antony put Betis in front after 13 minutes and Abde Ezzalzouli bagged their second in the 26th minute.
But Pau Victor reduced the deficit with Braga’s first shot on target in the 38th minute and Vitor Carvalho equalised four minutes after half-time.
Braga’s Ricardo Horta calmly converted a 53rd minute penalty and Jean-Baptiste Gorby’s 74th-minute goal completed the Portuguese side’s stirring fightback.