Chelsea, holding a 2-1 first-leg lead, wrapped up an evenly balanced tie after 69 minutes when Joe Cole scored with a brilliant volley after a long raking pass from Florent Malouda.
Earlier Nicolas Anelka hit the Everton crossbar while Joleon Lescott went close for the home side after only 10 minutes but saw a fine header scrambled away by Chelsea keeper Petr Cech.
Spurs reached the final on Tuesday when they ended an eight-year winless streak against Arsenal, thumping them 5-1 at White Hart Lane to earn a 6-2 aggregate triumph.
The only other occasion Chelsea and Tottenham have met in a major final was in 1967 when Spurs won 2-1 in the first all-London FA Cup final at Wembley Stadium.
They were due to meet at White Hart Lane in a Premier League match on Feb. 23 but instead will face each other in the first League Cup final at the new Wembley the following day.