The Hammers, relegated last season, are now just 90 minutes from an immediate return to the top flight after goals from Kevin Nolan, Ricardo Vaz Te and Nicky Maynard swept aside Cardiff 3-0.
Having led 2-0 from the first leg, West Ham finished the job in style with a 5-0 aggregate success and will now face either Blackpool or Birmingham on May 19 - the club's first trip to Wembley in 31 years.
Upton Park boss Allardyce said: "The away game gave us the platform and this performance, to top it, was terrific.
"I'm pleased for all the players, the staff and the fans.
"We've got a massive opportunity over 90 minutes to get back into the golden league, where it all happens.
"Hopefully we can hold it together and give a performance like we did today when we get to Wembley.
"It's a big pressure for us and whoever we get we will probably be favourites again, but what a fantastic stage to go and play on."
Both teams knew the importance of an early goal, Cardiff to haul themselves back into the tie and West Ham to kill it off.
And it was West Ham who struck the crucial first blow after 15 minutes, skipper Nolan nodding in the rebound after Carlton Cole's header was blocked by Mark Hudson.
They doubled the lead five minutes before the interval when Vaz Te skipped behind Stephen McPhail and rifled the ball across David Marshall.
And substitute Maynard had the final say with a superb finish from Henri Lansbury's through-ball a minute from time.
Player of the year Mark Noble, the only survivor from the Hammers side which won the play-off final at the Millennium Stadium in 2005, said: "Everyone says it's the biggest game in football and it's a great feeling to have made it.
"We deserve it and I'm sure everyone will enjoy the trip to Wembley."
The only down side for West Ham was an injury to Jack Collison, the two-goal hero of the first leg, who dislocated his shoulder and is a major doubt for the final.
As for Cardiff, they began the season with victory at Upton Park but ended it suffering play-off heartache for the third successive year.
It could have been different had referee Mike Dean not waved away an early penalty claim when Winston Reid sent Kenny Miller tumbling to the floor.
Manager Malky Mackay said: "I've not seen it again, but little things change games.
"But West Ham were clinical today. We're obviously disappointed, but we knew it would be a tough task.
"Congratulations to West Ham, they deservedly got to the final and good luck to them."