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.’’
WEST HAM: Green, Demel, Tomkins, Reid, Taylor, O’Neil, Noble, Nolan (McCartney 69), Collison (Lansbury 48), Cole (Maynard 86), Vaz Te.
CARDIFF: Marshall, McNaughton (Blake 81), Hudson, Turner, Taylor, Lawrence, Gunnarsson, Whittingham, McPhail (Cowie 76), Mason.
Ref: Mike Dean (Wirral).