Ronaldo and Messi vied for the right to lay claim to being Europe's best player during the nine years the former Manchester United forward spent at Madrid, but Valverde said his €112 million (£100m) switch to Serie A calls time on the pair's tussle.
Madrid finished third in La Liga in 2017-18, 17 points behind Valverde's champions - who also won the Copa Del Rey - but the Barca coach suggested this season would usher in a new era in Ronaldo's absence.
"Ronaldo leaving would seem to have ended the competition between Leo Messi and Cristiano Ronaldo because people rarely mention one without mentioning the other," Valverde told the club's official magazine, Barca.
"A lot of people are interested, me too, to see how it will affect Real Madrid's football and what they might do in the transfer market.
"Also, knowing that Ronaldo is at another club and what that might mean for LaLiga and the Champions League too."
While Barcelona have been on top domestically, Madrid have won the Champions League in four of the past five seasons, with Ronaldo typically inspirational in their successes.
Despite a domestic double, Valverde's first season in charge was marred by Barca's shock Champions League exit at the hands of Roma in the quarter-finals.
After taking a 4-1 lead into the second leg, Barca were beaten 3-0 and exited the competition on away goals at the Stadio Olimpico, with Valverde demanding greater focus in such situations.
"We had a horrible day against Roma and we have to be careful in those one-off situations," he said.
"In competitions like those, the Champions League or the World Cup, it can all come down to a single mistake on a single day. You have to be especially focused.
"I'd like to keep the same team spirit that we had last season. It's not always easy to do that throughout a whole season, especially in a team like ours that always plays to attack.
"Opponents generally haven't stopped us playing in matches and that's essential if you want to maintain your consistency and end up as champions. I think we have to keep that."
He added: "We made a huge effort to always stick together, both in attack and defence."