Late goals by Pernille Harder and Fran Kirby took Chelsea through to their first Women’s Champions League final.
The Blues trailed 2-1 after the away leg but Kirby put them in control on away goals.
Two goals from Lieke Martens gave Barcelona a second-leg victory over Paris St-Germain which sent them through to the Women’s Champions League final.
Barcelona won 3-2 on aggregate and will play Chelsea – 5-3 aggregate winners over Bayern Munich – in the final.
Chelsea will face Barcelona, who beat Paris St-Germain 3-2 on aggregate in the other semi-final, in the Gothenburg final on Sunday, 16 May.