Manuel Pellegrini's side had already effectively booked their place at Wembley after winning the first leg 6-0 at Eastlands, but they didn't take it easy in the return at Upton Park.
Alvaro Negredo and Sergio Aguero put City two goals up before half-time in east London and Negredo struck again after the break to cap another clinical display from one of the most potent strike-forces in Europe.
City will face arch rivals Manchester United in the final on March 2 if David Moyes' side can overturn a 2-1 deficit in the second leg of their semi-final against Sunderland at Old Trafford on Wednesday.
"It was a very professional performance. It was easy to think the game was finished from the 6-0 in the first leg, but it was important to reach the final winning all the games," Pellegrini said after his team had sealed the biggest ever winning margin in a League Cup semi-final.
"Wembley is always important. To me it is the same whoever we play there."
With City in possession of a seemingly unassailable advantage, Pellegrini made eight changes from the side that beat Cardiff in the Premier League on Saturday.
The impressive depth of City's expensively assembled squad was on full display as the Chilean was still able to field the likes of Negredo, Aguero, Jesus Navas and Fernandinho.
Hammers boss Sam Allardyce handed Andy Carroll his first start since the final game of last season after the England striker's long struggle with a foot injury.
Given the inevitability of City's progress to Wembley and, with an adult ticket for the match costing pound sterling42, it was hardly surprising to see vast swathes of empty claret and blue seats around Upton Park.
The 20,000 stay-away fans couldn't be blamed and their decision looked even wiser as West Ham's creaky defence was breached with less than three minutes played.
City's teenage Portuguese winger Marcos Lopes had time and space to float a cross into the six-yard box, where Spanish striker Negredo rose completely unmarked to power a header past Jussi Jaaskelainen from close-range.
The muted City celebrations suggested even they were slightly embarrassed at the ease of both the goal and their path to Wembley.
West Ham's Kevin Nolan had the ball in the net moments later but his strike was ruled out for offside and City were quickly back on the attack as Aguero fired into the side-netting.
Aguero, making his first start since December after a calf injury, threatened again with a surging run and shot which Jaaskelainen pushed away for a corner.
But Aguero wasn't to be denied for long as the Argentine forward punished more woeful West Ham defending to increase City's lead in the 24th minute.
West Ham centre-backs Roger Johnson and James Tomkins stood statuesque as the impressive Lopes advanced into the penalty area, where the ball ran for Aguero to calmly sweep a low shot past Jaaskelainen for his 22nd goal of the campaign.
Aguero's class is undeniable but he showed the ugly side of his game soon after when he was fortunate to escape with a yellow card for a stamp on Tomkins.
Allardyce surrendered at half-time as he took off Carroll to keep him free from injury for the more important task of saving West Ham from relegation.
West Ham held the record for the most goals scored in a League Cup semi-final, when Martin Peters, Geoff Hurst, Bobby Moore and company racked up a 10-3 aggregate win over Cardiff in 1966.
And City had that achievement in their sights when Negredo barged his way through the Hammers defence once again before stretching to clip his shot over Jaaskelainen in the 59th minute for his 23rd goal of the season.
In the end, City settled for just three goals and their thoughts had already turned to Wembley long before the final whistle put West Ham out of their misery.