Leeds were beaten by the Gunners in the final of last season's FA Women's Cup, but Julie Chipchase's side will be given the chance to exact their revenge when they renew hostilities with Arsenal on March 4th.
The semi-final victory over Charlton continued an outstanding run of form from United.
Chipchase said: "This was a wonderful team effort right through from the players to the staff and the supporters. The girls were tremendous. Everyone dug in and worked so hard.
"We knew the last time we played Charlton we didn't do ourselves justice, and I thought we were very unlucky not to have won the tie in normal time.
"It's a fantastic achievement for the club to have got through to their second final in 2006. We don't have the resources of Arsenal or Charlton, but we do have excellent team spirit and good quality players who all have ambition and hunger."
Charlton have reached the last three League Cup finals and were heavy favourites to make a fourth straight appearance, but United produced a vastly improved performance having lost 5-3 to the London club last month.
Chipchase was critical of her players' first display against Charlton, but United's boss had no complaints after their outstanding result at Gravesend on Sunday.
Leeds were forced to overcome the loss of Sue Smith, who sustained an injury in training ahead of the semi-final, but replacement Jess Clarke made an immediate impression by creating the opening goal after 12 minutes.
Her cross was headed home by Lucy Ward from close range, and the strike was the perfect start to a tough fixture.
Charlton created a handful of first-half chances but, with the game heading for the interval after four minutes of injury time, Gemma Ritchie volleyed home Michelle Hickmott's delivery at the far post.
The strike gave Charlton momentum at the start of the second period, and the game turned against United when Natasha Dowie gave the hosts the lead with 56 minutes gone.
But a brilliant strike from Nicole Emmanuel dragged Leeds level with 15 minutes remaining, and Charlton were left hanging on as Chipchase's side pushed for a late winner.
A goalless period of extra-time forced both sides into a penalty shoot-out, however, and Ritchie and Karen Hills failed from the spot as United claimed a 4-3 win.