The Bundesliga champions cruised to a 3-0 success in their semi-final second leg at Camp Nou to complete an astonishing 7-0 aggregate triumph.
Robben and Thomas Muller were both on target with Gerard Pique putting through his own net on a miserable night for the Catalan giants, who left Lionel Messi on the bench throughout the contest.
Bayern, who have suffered final heartache at the hands of Chelsea and Inter Milan in recent years, will now take on domestic rivals Borussia Dortmund at Wembley on May 25.
Robben told Sky Sports: "Now we are in the final, it is the third time in the last four years, but it is time to win it now.
"It is going to be a big one. Dortmund have proved over the last two or three years that they are a very good side. It is going to be a game which is decided on small details.
"I think we have to stay calm. We are playing some great football, we have to enjoy this moment."
Bayern were superior to Barcelona in every department over both legs, with Robben pointing to their impressive team ethic and work-rate as one of the key reasons for their success.
He added: "The most important thing of all is we play as a team. Defensively we are very well organised, everyone is doing their job, also the four players up front work hard backwards.
"If you want to achieve something, if you want to win competitions and games at such a high level you have to defend as a team.
"If you perform like this, playing against a team who have dominated Europe over the last five years, if you win 4-0 and 3-0 away, it is amazing.
"Especially against a team like Barcelona you cannot give them any space to play. They didn't really have any good chances."