Chelsea, who will play either Fulham or Liverpool in next month's final at Wembley, thrashed Championship club Middlesbrough 6-1 in the second leg of their semi-final at Stamford Bridge. Middlesbrough had won the first leg 1-0.
The 51-year-old Argentine, who previously managed Tottenham, Southampton and Espanyol, won Ligue 1 with Paris St Germain in the 2021-22 season. He also guided them to the French Cup and Trophee des Champions.
Pochettino came close to success with Spurs twice when they finished runners-up in the League Cup (2014-15) and Champions League (2018-19).
"I'm desperate to win a title here," Pochettino told reporters. "In one year and a half in Paris, we won three trophies, and we want to win one here. I'm desperate to win, of course.
"In some point, it's an amazing achievement. I think it was the objective when we started: with no Champions League, no Europa League, no Conference League, to build a team from nearly zero.
"The job is done but now it is about winning the final."
Chelsea are ninth in the league after 21 matches. They next host Aston Villa in the fourth round of the FA Cup on Friday.
