Negotiations between the two clubs have run for several weeks, with an initial gap in valuation finally narrowed following a breakthrough last week.
The London Evening Standard reports the fee at an initial £16.2 million plus a further £1.7 million in add-ons, though other reports in Spain and England have varied significantly, with some outlets citing figures as high as £16.3 million and others putting the total closer to €25 million.
A medical is understood to have been booked as Chelsea prepare to complete the move.
Chavarría, who joined Rayo Vallecano from Real Zaragoza in 2022, made 125 appearances for the Madrid club and played every minute of their run to last season's Europa Conference League final, where they lost 1-0 to Crystal Palace. He will compete with Jorrel Hato for a starting spot at left-back following Marc Cucurella's departure to Real Madrid, with Marco Palestra occupying the opposite flank after his own arrival from Atalanta.
Chavarría's move comes as Chelsea also confirmed the departure of goalkeeper Filip Jörgensen, who has joined sister club Strasbourg on a season-long loan. Jörgensen had grown increasingly keen to leave Stamford Bridge this summer after being restricted to just 36 appearances across two years following his move from Villarreal.
"Jörgensen was a key member of the Chelsea side that lifted the UEFA Conference League in May 2025, starting all but one game in the competition," Chelsea said in a statement.
"The Denmark international became a Club World Cup winner later that summer. Jörgensen featured 12 times last season across four different competitions, playing his part as we reached the semi-finals of both domestic cups. We look forward to supporting Filip throughout his time in France."
The goalkeeper's exit continues a busy summer of outgoing business at Stamford Bridge, following the departures of Andrey Santos, Alejandro Garnacho, Tyrique George and Trevoh Chalobah.
Pedro Neto, Malo Gusto, Josh Acheampong, Liam Delap, Nicolas Jackson, Axel Disasi, Benoît Badiashile and Marc Guiu are among those who could follow through the exit door before the window closes, as Alonso continues to reshape his squad around the new arrivals.