Sources told ESPN that the deal includes the option to buy it next summer for a set fee.
The deal was questioned as none of the clubs confirmed the transfer before midnight CET.
Local media said the delay was caused by a problem with LaLiga’s transfer check-in system and the documentation was provided on time correctly.
“We welcome Sol to the club and believe he has joined our team as we compete for awards in five different competitions this season,” said Chelsea Director Marina Granovskaya.
“He is a proven winner, a player with a lot of experience, and we know he will be very well adapted to the challenges we face on all fronts in the coming year.”
ESPN recently reported Chelsea was in talks with Sol, while Manchester United were also interested in Spain midfielder who spent the last 13 years at Atlético after going through the club’s youth ranks.
However, United backed out of the deal, giving Chelsea the opportunity to strike a second major deal this summer after Romelu Lukaku left Inter Milan for a € 115 million deal.
This material uses information from Reuters.