The Sweden international last week completed a £3million switch from Roma after spending the second half of the season with the club on loan.
Olsen, who has been signed to provide competition for Villa No.1 Emi Martinez, believes his game has already improved during his time in the Midlands.
After spending the bulk of the last three seasons on loan with Cagliari, Everton and Sheffield United before Villa, he is looking forward to putting down some permanent roots.
Speaking while away on international duty with Sweden, he said: “It’s a new adventure, so to speak. Now we know that we will stay there (at Villa) for three years.
“It’s a fantastic club and incredibly nice that it’s been resolved. I feel how much I’ve developed in just the five or six months I’ve been there. We started talking early about triggering the clause, but then a few other things made it take time. It’s very nice it was resolved.”
Villa have made a quick start to their summer business, signing Philippe Coutinho, Boubacar Kamara, Diego Carlos in addition Olsen and selling Matt Targett to Newcastle.
The latter’s £15million move means a new left-back will be targeted in order to provide cover and competition for Lucas Digne.
Boss Steven Gerrard would also like to recruit up front but a deal for West Ham youngster Sonny Perkins is not on the agenda.