The Londonders, in front of their Upton Park home crowd, won 3-0 on Monday for a 5-0 aggregate victory.
They will now face either Birmingham City or Blackpool — both also relegated last term, and who conclude their playoff semifinal on Wednesday — in the playoff final at Wembley on May 19.
The match is often billed as “the richest game in football” as a place in the Premier League is worth an estimated £90-million to the winning club.
Having suffered the disappointment of missing out on automatic promotion behind Championship winners Reading and runners-up Southampton, West Ham wasted little time feeling sorry for themselves.
They came into Monday’s match on the back of a 2-0 first-leg win in Cardiff courtesy of two Jack Collison goals and the tie was put beyond any lingering doubt when midfielder Kevin Nolan opened the scoring in the 15th minute.
Ricardo Vaz Te made it 2-0 five minutes prior to the break before Nicky Maynard set the seal on an emphatic victory with a 90th-minute goal against a Cardiff side already beaten by Liverpool in this season’s League Cup final at Wembley.
West Ham manager Sam Allardyce told Sky Sports: “The response at Cardiff and this performance were terrific. I’m pleased for everybody concerned with West Ham United.
“We have a huge opportunity to get into the golden league, not for the money from my point of view, but because that is where it all happens.”
As for the final, Allardyce added: “It is big pressure for us. Whoever we get, whether it is Birmingham or Blackpool, we are probably going to be favourites and we have to live with that.
“Hopefully the players can look forward to it and deliver another outstanding performance.”
For Cardiff defeat meant yet more playoff heartache, having lost in the semifinals to Reading last season after being beaten in the 2010 Championship playoff final by Blackpool. — Sapa-AFP