Bilbao qualified for Europe's premier club competition with a routine 3-0 victory at Rayo Vallecano in La Liga on Friday.
Goals from Mikel San Jose, Oscar de Marcos and Ander Herrera were enough to seal fourth-placed Bilbao's first Champions League berth, albeit in the qualifying stages, since the 1997-98 campaign, when they finished nine points adrift of winners Barcelona.
Nearest rivals Sevilla are nine points behind with three games to play but they are unable to overhaul the Basque club due to their inferior head-to-head record.
"It's a huge joy, getting the opportunity to play in the Champions League," said Valverde after the match.
"It's true that we were all very tense, we took the game that way, but now we're in heaven.
"We knew Rayo were in good form, but we wanted to assert our own needs."
Most pleasing for Valverde was Athletic's ability to challenge the big guns on the back of their official policy to only recruit and promote players from the Basque region.
"For a team like Athletic to be behind Atletico Madrid, Barcelona and Real Madrid in the league table is a triumph and even more so because of the special philosophy of this club," he said.
"We have a different philosophy when it comes to finding players and for that reason, we have to fight, be more united and we have to demonstrate a different way of competing."
While Athletic have sewn up fourth position, Valverde has no intention of letting his players take their foot off the pedal during the final two games of the season against Real Sociedad and Almeria.
"For us it's a success to get into the qualifying stage of the Champions Leaguebut we've got another challenge before that and it's to get as many points as we can, adding continuity to what we're capable of doing," he added.
