Emma Hayes' side completed a domestic double having clinched the league title recently.
Liverpool won 6-5 in shootout after it ended 0-0 at the end of extra time.
Second-half goals from Ruben Loftus-Cheek and Mason Mount fired Thomas Tuchel's side to victory in the semifinal and secured a place in the May 14 showpiece match versus Liverpool, who beat Manchester City 3-2 on Saturday.
The Reds hung on to beat Manchester City 3-2 at Wembley Stadium to reach the final of the FA Cup.
Tielemans's goal will count among the finest to win this 149-year old competition.
The 2-1 victory over Chelsea earned Arsenal a record-extending 14th crown in the competition - and a spot in next season's Europa League.
Chelsea, who face rivals Arsenal in the August 1 (Saturday) showpiece, had lost to United three times this season but dominated the match and took control with goals either side of half-time from Olivier Giroud and Mason Mount.
Standing in the way of Arsenal's 14th FA Cup triumph and a trophy for Arteta in his first season as a manager will be either Chelsea or Manchester United who play on Sunday.