The Hammers quickly shrugged off the disappointment of missing out on automatic promotion as goals from Kevin Nolan, Ricardo Vaz Te and Nicky Maynard booked them a trip to Wembley for the first time in 31 years.
One year on from relegation, they will now face either Blackpool or Birmingham on May 19 for a shot at returning to the top flight and the estimated £90million reward promotion brings.
As for Cardiff, they began the season with victory at Upton Park but ended it suffering play-off heartache for the third successive year.
Malky Mackay's side arrived in east London as huge underdogs, trailing 2-0 from the first leg in Wales last week.
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 the visitors did pose a brief threat, having a half-hearted penalty appeal turned down when Kenny Miller tumbled under Winston Reid's challenge.
But it was West Ham who struck the crucial first blow from Matt Taylor's 15th-minute corner.
Carlton Cole's close-range header was blocked by Cardiff skipper Mark Hudson but Nolan was on hand to nod the rebound over the line for his 13th goal of the season.
It was one-way traffic from then on with a disappointing Cardiff side already resigned to their fate.
West Ham were inches from going two up when Jack Collison, the two-goal hero from the first leg, crossed to Gary O'Neil, whose first-time volley came back off the bar.
O'Neil then forced a fine diving save from David Marshall with a swerving effort from outside the area.
And five minutes before the interval the hosts did double their lead in style.
Cardiff defender Stephen McPhail missed Guy Demel's pass but Vaz Te did not, taking the ball in his stride before blasting an unstoppable angled drive past Marshall and into the net.
After the break Taylor and Reid had shots blocked while a rare Cardiff foray forward saw Liam Lawrence drive wide.
But it was Hammers substitute Maynard who had the final say with a superb finish from Henri Lansbury's through-ball a minute from time.
The jubilant home fans burst into a rendition of 'we're going to Wembley' - and they actually meant it for the first time since Trevor Brooking, Billy Bonds and Co lost the League Cup final to Liverpool way back in 1981.
