Midfielder Sergi Darder said he was looking to depose French champions Paris Saint-Germain after joining Lyon from Spanish club Malaga.
Darder, 21, signed a five-year contract after the clubs had agreed a €12 million fee.
The Spain under-21 international confirmed that PSG had also tracked him this summer -- but that he now wanted Lyon to rival them for silverware.
"With PSG, it was an interest on their part rather than any advanced contacts," he told L'Equipe.
"In terms of the sporting rivalry, a budget doesn't decide everything. Look at Atletico Madrid, who were champions of Spain in 2014 ahead of Real and Barca. These type of performances are one of my aims here. I want to win trophies."
Darder is Lyon's biggest signing in five years but said he had feared the move would not go through after negotiations hit a snag.
"At one point everything seemed to be done," the former Espanyol player said.
"I had confirmation -- and then it fell through. After this incident, I started losing weight and I wasn't sleeping any longer... but that's in the past. What matters is that today I'm at Lyon, one of the biggest clubs in the world."
Darder was presented to the media on Monday along with France under-19 midfielder Lucas Tousart.
Tousart, 18, has joined from Ligue 2 side Valenciennes and cost Lyon €2.5m.