Cardiff, who are 14th in the Championship, are also due to host 19th-placed Barnsley on the last day of the season at Ninian Park on 4 May.
Barnsley's Swansea-born manager Simon Davey told BBC Radio 5 Live that all four teams should believe they can win the FA Cup this season.
"All of us think we can go on and win the competition," said Davey. "We've drawn Cardiff, we are both Championship clubs and we'll both be thinking it's a great opportunity to get to the final.
"We know a lot about them and they know a lot about us so I'm sure it'll be a great occasion and it will be an entertaining game."
Barnsley chairman Gordon Shepherd revealed the Tykes' FA Cup run would earn the club £2.6m if they could overcome Cardiff in the last four.
He said: "We've probably made up to now, with winners' bonuses so far and gate receipts and things, around £1m.
"We think once we've played the semi-final it will probably be worth another £700,000.
"However, if we won the semi-final we'd get a £900,000 winners' bonus as well, so there's a lot at stake, there really is."
Cardiff boss Dave Jones added: "To be in the semis is a great achievement for this football club and to be honest it didn't really matter who we were paired with.
FA CUP LAST FOUR FACTS
1908: Last time three non-top flight teams reached semis
1912: Barnsley's FA Cup win
1927: Cardiff's FA Cup win
1939: Portsmouth's FA Cup win
1968: West Brom's last FA Cup win - their fifth triumph
2004: Last time a team from outside Premier League reached final (Millwall)
"They are bound to be confident after their two great results and we will be after our performance at Middlesbrough on Sunday."
The draw means Barnsley's on-loan keeper Luke Steele can play at Wembley - had the Tykes been paired with his parent club West Brom, FA rules would have prevented him from playing.
West Brom boss Tony Mowbray said his side were relishing the task of facing Harry Redknapp's Portsmouth.
"I had no preference as to who we drew because any semi-final is a tough game," he said.
"Harry has built a powerful side who are enjoying a terrific season.
"We're very respectful of the talent they possess but we've earned the right to play this game and we're looking forward to the challenge."
After a weekend of sensational results, it means a club apart from Manchester United, Arsenal, Liverpool and Chelsea will win the tournament for the first time since Everton in 1995.
It will also be the first final between two teams outside the 'big four' since Tottenham beat Nottingham Forest 2-1 in 1991.
If anyone other than Portsmouth lifts the trophy, it will be the first time since West Ham beat Arsenal 1-0 in 1980 that a team outside the top flight gets their hands on the Cup.
FA director of communications Adrian Bevington said: "I'm sure the supporters of all the clubs are so excited because they've not been to Wembley for a very long time.
"I know there will be a fantastic level excitement building among all supporters' groups."
As it stands, if Cardiff win the Cup they will not be allowed to enter the Uefa Cup, as Uefa regulations prevent the Welsh side from playing in European competition as England's representative.
Draw for FA Cup semi-finals:
Barnsley v Cardiff West Brom v Portsmouth
Simon Davey's side proved their 2-1 win over Liverpool at Anfield in the fifth round was no fluke by beating holders Chelsea 1-0 at Oakwell.
Despite hovering four points above the Championship relegation zone, the Tykes will be making their first appearance in the semi-finals since 1912, the year they lifted the trophy after a win over West Brom.
Path to the semi-finals: Third round: Barnsley 2-1 Blackpool Fourth round: Southend 0-1 Barnsley Fifth round: Liverpool 1-2 Barnsley Quarter-finals: Barnsley 1-0 Chelsea
The FA Cup has provided a welcome distraction for Cardiff's faltering bid to reach the Championship play-offs and their problems off the pitch.
Bluebirds manager Dave Jones has urged his team to make their own piece of FA Cup history in their first semi-final appearance since their famous Cup victory of 1927.
Path to the semi-finals: Third round: Chasetown 1-3 Cardiff Fourth round: Hereford 1-2 Cardiff Fifth round: Cardiff 2-0 Wolves Quarter-finals: Middlesbrough 0-2 Cardiff
As the Premier League's solitary representative left in the competition, Portsmouth will be favourites to go all the way.
Pompey boss Harry Redknapp will certainly fancy his chances of taking Portsmouth to their first FA Cup final since 1939.
Path to the semi-finals: Third round: Ipswich 0-1 Portsmouth Fourth round: Portsmouth 2-1 Plymouth Fifth round: Preston 0-1 Portsmouth Quarter-finals: Manchester United 0-1 Portsmouth
West Brom have a fine FA Cup tradition after winning the competition five times and appearing in the final on 10 occasions.
Albion manager Tony Mowbray will claim promotion is his main objective but the Baggies are now second favourites to lift the trophy.
Path to the semi-finals: Third round: Charlton 1-1 West Brom Third round replay: West Brom 2-2 Charlton (West Brom won 4-3 on penalties) Fourth round: Peterborough 0-3 West Brom Fifth round: Coventry 0-5 West Brom Quarter-finals: Bristol Rovers 1-5 West Brom
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