Chavarria has signed a deal until 2031 at Stamford Bridge as Xabi Alonso looks to fill the void left by Marc Cucurella's switch to Real Madrid prior to the 2026 FIFA World Cup.
The final deal between Chelsea and Rayo is rumoured to have reached a final figure close to €23M (£19.6m), including add-ons, as the Chelsea refused to pay his €50M (£42M) release clause in Madrid.
The 28-year-old made over 150 appearances across four season at Rayo including a run to last season's Conference League final where they lost out to Crystal Palace.
As part of his first interview as a Chelsea player, Chavarria revealed how the chance to test himself in the Premier League and a key conversation with Alonso, convinced him to make the move to London.
"I've played in Spain all my life, but the Premier League is the best league in the world right now. There's lots of quality and intensity, so I think it's the best league for me.
"I've already spoken with Xabi Alonso, I'm here thanks to him. He's one of the best coaches out there right now and he was also one of the best footballers. It's an honour to be here playing under him."