Giroud, who won the trophy three times with Arsenal, struck in the first minute of the second half, slotting home from close range after weaving through Southampton's defence.
Alvaro Morata came on from the bench to wrap up the victory late on, sending Antonio Conte's side through to a second successive FA Cup final, where Manchester United and former Blues' boss Jose Mourinho will be their opponents.
"I told my team-mates that I really wanted them to enjoy the FA Cup because I know what the feeling is to win here," Giroud, part of the Arsenal team that defeated Chelsea in last year's showpiece, said to BT Sport.
"Playing [at Wembley] is like playing in my garden, I love to play here and love to win here.
"Eden [Hazard] gave me a good ball but I saw a lot of players in front of me. I tried to dribble a bit, I had a bit of luck but that's what I wanted to do.
"At the end of the day I'm pleased for the team, we have done a good job together, what we wanted to do.
"We have four games left to play in the league, we put the FA Cup to the side and focus on that."
Hazard put in a wonderful individual display at Wembley, the Belgian showing the kind of form that saw him propel Chelsea to the Premier League title last term, and said the Blues executed Conte's gameplan down to a tee.
"I think we played a very good game, especially in the second half. We created a couple of chances and scored beautiful goals," Hazard said.
"Now we know the target. We lost last year and now we just want to win it.
"[Conte] told us to keep the ball, just keep the ball and play our football and then create a chance. When you score early in the second half the game is easier, you control the game, create chances and get the result.
"It's always good to play against Manchester United. They won at Old Trafford so to do it in a final will be a great game."